A person who is neither a theist, nor an atheist (nor, for that matter an agnostic).

A nontheist neither believes God exists, nor that God does not exist.

To a notheist, both theism and atheism are a complete waste of mental bandwidth. In other words, to a nontheist the question of the existence or non-existence of God is completely irrelevant.

A nontheist is different from an agnostic: An agnostic generally believes we simply cannot know whether God does or does not exist. A nontheist, on the other hand, generally believes that it is possible to figure it out, but why bother?

The Buddha is the first historically known nontheist. Most Buddhists are nontheist.

The Buddha was often asked whether God existed. Usually, he replied with a complete silence. Once, however, he told the story of the man shot by a poisoned arrow.

When the doctor came and wanted to pull the arrow out of the wound, the man grabbed the doctor's hand and asked:

"Before you start treating me, Doctor, tell me, who was it that shot me? Was he of warrior class or some other class? Was he tall or was he short? Was he young or was he old? Was he dark skinned or light skinned?"

The doctor ignored the questions and pulled the arrow out. Had he answered the questions, the patient would have died.

That is why, said the Buddha, I will not answer your question about God. If I did, you would just spend your time in endless speculation, and never awaken from your current state.