Apatheist and ignorestic are slang terms that describe a person who is technically an atheist (does not believe in a god) but does not approach atheism from a rational point of view and has not considered many religious or apologetic arguments.
Apologists who claim that "I used to be an atheist" are very likely to have been apatheists. Usually their conversion story does not involve a change in their intellectual understanding of the arguments, but instead revolves around an emotional experience or a first encounter with unfamiliar apologetics.
Apatheism is also a term used to describe those who adopt the position that the belief in a god and religion are irrelevant when evaluating your own actions or the actions of others.
An Apatheist in essence believes that because the existence or non-existence of a deity is impossible to prove conclusively through rational and scientific means, human beings need not concern themselves with the issue of divinity or religion, when evaluating actions. Whatever the source of a person's belief, it is the actions of a person which matter.
Some apatheists, especially those who can be described as agnostic atheists, even take it a step further. Those who fit this categoty typically don't believe there is a deity. But even if someone could prove through tangible, repeatable, predictable, and scientifically-verifiable means that there in fact was a deity as described by scripture-based religions (Judaism, Christianity, Islam) it still would have no effect on how they lead their lives. These apatheists would not honor or follow such a deity, as they would consider it an egocentric, sadistic, and generally cruel being.
The apatheistic philosophy could be summarized simply by the following statement: "We don't know and we don't care!"
Another statement that is associated with Apatheists is the following when referring to the question of whether a deity exists: "The question is no longer important; the answer is no longer interesting."
The term Apatheism was first used by Jonathan Rauch in an article published in The Atlantic. In that article, he briefly defines the position as follows:
"To be in the grip of religious zeal is the natural state of human beings, or at least of a great many human beings; that is how much of the species seems to be wired. Apatheism, therefore, should not be assumed to represent a lazy recumbency, like my collapse into a soft chair after a long day. Just the opposite, it is the product of a determined effort to discipline the religious mind set, and often of an equally determined personal effort to master the spiritual passions. It is not a lapse. It is an achievement."