Existence of Jesus
The existence of Jesus as a real, historical figure has been debated for centuries. Apologists who believe Jesus did actually exist try to use this purported fact to support other claims, such as that he was divine or that his teachings should be followed.
Historical vs. biblical Jesus
When debating the question of whether Jesus really existed, it is necessary to distinguish between several questions: "Was there a preacher named Jesus in Judea around 1-33 CE, who was crucified by the Romans?" and "Was there really a person who performed the miracles attributed to Jesus in the Bible?" The former is an ordinary and plausible claim; the latter is an extraordinary claim, and requires extraordinary evidence. This is like asking "Did George Washington exist?" vs. "Is it true that George Washington threw a silver dollar across the Potomac river?"
If Jesus was an ordinary human who did not perform any miracles, it would not be surprising that there are no contemporary accounts of his existence, since most people from that era have gone unrecorded.
However, if he had performed miracles, or if his life had been accompanied by extraordinary events, we would expect many people to have written about them. For example, Matthew 27:51-51 says that when Jesus died, many dead people came back to life "and went into the holy city, and appeared unto many." The fact that there is no extrabiblical record of such an extraordinary event strongly suggests that it never happened. Likewise, the star of Bethlehem, which allegedly marked Jesus' birth, would presumably have been seen all over the world, and been recorded by other literate societies, such as China.