The Israelites are the people of the nation of Israel.
History of Israel and early Jewish religion
The Israeli people and religion grew gradually and have a complex history. The earliest mention of Israelites is in the Merneptah Stele, depicting and glorifying the military conquests of this pharaoh in the late 13th century BCE. Amongst other things, it describes a military journey to Canaan, probably to the central mountain region, where the kingdom of Israel would later reside. Merneptah boasts that "[the people of] Israel is laid waste; its seed is no more". While this is clearly an exaggeration, it does attest to the existence of a group of people called Israel in Canaan as early as the late 13th century (circa 1207).
At this time the people of Israel are indistinguishable from other Canaanite groups and seemed to have shared the same polytheistic religion (although the names of the gods were local and differed between Canaanite groups). The only major difference that can be traced back to these times (Iron Age I, 1200-1000 BCE) is the disappearence of pig bones from the highlands, that may indicate a distinguishably Israelite custom and, perhaps, religious taboo. There was still no apparent writing, but Biblical Criticism indicates that it is probable that by this time early tales of an Egyptian exodus (perhaps memories of the Hyksos period, where the Canaanites controlled the Nile delta) were already told orally. Similarly, tales about the eponymous forefathers arose at this period, partly out of local legends to explain local sites (such as gigantic constructions left from the Bronze Age) and partly as memories of the actual deeds of forefathers, including perhaps some immigrants from Mesopotamia or Syria. Despite such tales, the majority of Canaanites, including the Israelites, were of local stock, and Israelite culture coalesced locally.
Iron Age I (1200-1000 BCE) and the early part of Iron Age II (1000-856 BCE) saw an increase in population as favorable climatic conditions led to the emergence and increase in international trade. Local warlords squabbled between each other, and tales of heroism abounded, the most famous of which is the David and Goliath story.
By the middle of the 10th century BCE a kingdom in the central mountain, with Samaria as its capital, emerged. It would come to be known as The Kingdom of Israel, but at that time it was known as "Beit Omri" ("The [Kingdom founded by the Royal] House of Omri"). The Israeli kingdom vied with Aram, the kingdom led from its capital Damascus, over the northern valleys of Galilee and Gilead. It eventually came into conflict with the Assyrian empire, which wiped it off the map at 722 BCE. The ruling elite and much of the population of Samaria and the surrounding heartland of the kingdom were exiled, and foreign population was settled in the southern regions of the kingdom.
The Kingdom of Israel maintained a polythesitic and decentralized religion till the end. While at its height it included many Phoenician, Moabite, and other Canaanite factions besides Israelites, it did not impose its culture on them and allowed their religions to continue unabated. Biblical condemnations maintain that it retained the worship of idols, and there is no reason to doubt that.
Concurrently, by the 9th century the House of David had gained control over the southern mountainous region, with its capital in Jerusalem. The resulting Kingdom of Judea was weaker than the northern kingdom and for the most part was subservient to it. After the destruction of the northern kingdom, however, it - and especially Jerusalem - was flooded by refugees, at numbers equal or exceeding the original Judean population. This led to a substantial religio-political reform that marked a turning point in Jewish and Western history.
The destruction of the kingdom of Israel was triggered by its revolt against the Assyrian king. As Judah, in contrast, remained a loyal vassal, it was rewarded and flourished under the reign of king Ahaz (reigned 735-715). As part of his acceptance of the globalization brought about by the Assyrian empire, he accepted and maintained non-Israelite religions and incorporated them into its religious practice, including establishing statues for such "foreign" gods in the Temple. This period of cultural tolerance and economic flourishing ended, however when his son and heir Hezekiah (715-686) got into a fit of religious bigotry. He instigated religious reforms that included the removal of temples except the temple in Jerusalem, which increased his economical power (as he drew tribute through the offerings to the Jerusalem Temple), and broke at least some idolatrous statues and signs of pagansim. It must be emphasized that this was a henotheistic - single-god worship - revolution, not a monotheistic (single god existing) one. Notably, however, archaeology proves that idol worship continued unabated in private houses. Worse of all, when the Assyrian king Sargon II died (705 BCE) Hezekiah attempted a revolt against Assyria. The resulting Assyrian response halved the size of his kingdom and forced unbearable taxes on its dwindled economy, but the Assyrians chose not to destroy Judea completely. It also had a curious theological ramification - to spin the disaster off as a success, it was explained that Jerusalem was spared because of a Divine promise not to harm the city. Forever.
Fortunately, another "pro-globalization" king arose in his wake - Manasseh (reigned 696-643), perhaps the greatest Judean king. He again allowed polythesim and reintroduced it to the temple, and even built pagan temples. He traded extensively, and his exploits and fame were eventually incorporated into the (earlier) figure of King Solomon.
Unfortunately, his grandson Josiah (reigned 641-609) returned to religious zealotry. Coming to the throne as an 8-year-old child, he appears to have been raised to believe he was a Messianic figure that would restore his people to righteousness and greatness, with disastrous effects. Josiah either undertook or was swept up by the great Deuteronomic reform that altered Judaism significantly. The Deuteronomic writers compiled stories combining the northern traditions from the Kingdom of Israel that continued to develop in Judea with their own local traditions, creating the complex weave that characterizes the modern version of many of the Biblical stories - often involving two versions, and including both good and bad things about people. For example, they included the northern stories about the vices of David, the founder of the southern Judean kingdom, but also invented apologetics to explain them away; they included stories that put the legendary forefather of the northern kingdom, Jacob, as the descendant (and therefore lower in status) to the southern forefather, Abraham; and so on.
The most important revolution of the Deuteronomist however was the glorification of Josiah himself and his royal house, the House of David, and its combination with strict henotheism and xenophobia. On the negative side, the Deuteronomist vilified Manasseh's international achievements and conduct (even while attributing them to Solomon), which he associated with the promotion of paganism and idolatry he despised (as can be seen above, this was historically justified - the two were linked historically. This is why the book of Deuteronomy forbids a king from.... trading in horses, sending people into Egypt to purchase horses, and so on - all attributes of the rich trade in horses for Assyria under king Manasseh and, to a lesser extent, Ahaz and late Israelite kings. While incorporating many populist human-rights measures drawn from contemporary Assyrian laws, the book also contains strong admonitions against marrying foreigners and otherwise mixing with others and with their gods. In practice, this meant that Josiah intituted an even larger purge than Hezekiah, enforcing religious zealotry throughout his land.
The most disastrous aspect of this revolution was the positive side, however. Rewriting history, the Deuteronomist promised eternal rule to the House of David. He furthermore rewrote the Egyptian exodus stories and invented wholecloth the story-outline of the conquest of the land by Joshua to justify territorial claims over the entire formerly-larger kingdom of Judea and the now-destroyed kingdom of Israel. This lethal combination came to the fore when the mighty empire Assyria retreated from the Levant, leaving a power vacuum. King Josiah then made small advances into neighbors, ruining for example the temples at Beit El, a nearby holy place of the ancient kingdom of Israel.
His rampage of zealotry was cut short, however, by the Egyptian king Necho II, who while passing through the region easily killed Josiah. It is most likely that Judea was to be transferred to the Egyptian kingdom by the Assyrians, and Necho realized Josiah's madness and had him executed at his regional Imperial temple (newly passed over from the Assyrians) in Megiddo.
The death of the Messiah influenced the Isrealites rather badly. Messiahs aren't supposed to die. This originated longing for the king that would return from the dead - and thus was modern Messianism born. This is also the source of Armageddon - coming from "Har Megiddo", the mountain of Megido, where Josiah died, which will be the place of re-enacting the "battle", this time with the good side winning. Much of Christianity started with the death of Josiah.
The history of the Israelites still misses a key part - the change to monotheism, and eradication of the (still very strong) pagan version of Judaism. This was accomplished by the much more brutal Babylonian conquest. The puppet king installed by Necho soon switched sides to the rising Babylon, and then again to Egypt, resulting in a devastating Babylonian conquest. As if this wasn't enough, the successor Zechariah soon revolted again. The re-conquest was even more brutal, and Jerusalem and the Temple were destroyed. Yet there still remained many people in Judea. But the appointed governor, Gedaliah, wasn't of the line of David... as a result, he was assasinated by a member of the royal house that wanted to take his throne. Fearing Babylonian reprisal, almost all of the people fled to Egypt. And thus, in 582 BCE, the land was finally effectively deserted, and nearly all Israelites were in Babylonian and Egyptian exile.
The divine promise invented to cover up Hezekiah's downfall, that Jerusalem and the Temple therein will stand forever, has been destroyed. So have the promises that the House of David will rule there forever. To save the religion, the last great development happened - the vengeance of the Babylonians was seen as God's actions. YHWH was transformed into a vengeful universal god, that used Babylon as his pawn to punish Judea for it's unfaithful deviance in worshipping other gods.
With fanatic monotheism now in place and few in the land, when the Babylonian exiles returned under Cyrus the Great there was no longer any local polytheistic Jewish religion for them to contend with. All that was left was the monotheistic jealous and vengeful god that we all know and "love" so well.