Apatheism is apathy towards belief and disbelief in gods. An apatheist simply doesn't care whether there is or isn't a god. The word apatheism is a portmanteau of apathy and theism/atheism.

Apatheism can be described as the position that neither the existence nor the non-existence of gods is important, thus neither belief in nor denial of gods is important. For this reason, apatheism overlaps with pragmatic atheism and practical atheism.

Perspectives

On a practical level, apatheism refuses to say there is a God and also refuses to say there isn't a God. Apatheism is regarded as an attitude towards a type of belief, not a belief or disbelief itself.

An apatheist likely would disagree with anti-religious thinkers who seek to remove religious belief and practice. The apatheist attitude would be for freedom of religious belief and practice so long as there are no restrictions on being a non-believer. It is a position of tolerance without promoting religious belief or opposing it.

Resistant to Change

Apatheism sometimes goes a bit further and asserts that even if it were proven conclusively and without a doubt that some sort of god existed, then the person's general behavior and life would not change, For that person, the existence of gods is not only irrelevant now but would be irrelevant in the future no matter what sort of evidence or proof is present.

This form of apatheist would have to be very ingrained in habit or dedicated to their personal ethical system to say, "I see there definitely is a God, but I'm not changing." However, that is probably not much different from the behavior of nominal believers who continue to conduct themselves in ways prohibited by their religions. If they believe there is a God who will damn them to hell if they commit common sins like fornication and adultery but they continue to do so, their behavior not much different from what a committed apatheist's behavior would be.

Broader Definition

In some cases, apatheism is applied more broadly to all religions and even to all belief systems and ideologies, not just to belief and disbelief in the existence of gods. This broader sort of apathy and apatheism would be more correctly labeled Indifferentism, though because that label comes from Catholic theology it's not one familiar to most people.

Outside Perceptions

Atheists and theists might look at professed apatheists as being lazy thinkers who don't want to do the intellectual, philosophical, and emotional analysis to determine what they truly believe. Committed atheists and believers might be frustrated in any attempt to sway the professed apatheist to their side.

In social situations where the discussion of religion is frowned upon, the apatheist is perfectly happy and welcomed. An apatheist might attend religious ceremonies and appreciate the beauty of the music, religious art, and rituals without being bothered to take a position on whether the god or gods being worshiped exist.