1. A person who does not believe in a deity or God.

(In extreme cases, it is also a person who criticizes others for believing "fairy tales" from the Bible. These people are not atheists, as they would have you think, but elitists, and should be given a severe beating.)

Many people often confuse atheism with agnosticism, by saying that atheists are confused and have no faith whatsoever. This is not true. Although there are many different kids of atheists, the many principle is that there is no God or higher being. They do not always rely on science to come to this conclusion. Therefore, atheists do believe and have faith; they believe that there is no God and they have faith that God does not exist. Agnostics do not believe in God but they do not believe that there is no God. Atheism is often a teenage phase, but it also lasts for life. Some Atheists judge Christians, Jews, etc., but some do not, and I think it is very judgemental to classify all Atheists as "self-obsessed judgemental people who hate anyone who's not an atheist". In my experience, if you respect an Atheist's religion, they are, in most cases, more than likely to respect yours.

An Atheist is someone that does not believe in Gods.

A person who doesn't believe in god. Someone who doesn't believe that there is a heaven or hell. Close to an agnostic, who doesn't believe that either (god or darwinism) can be proven or disproven.

One who denys on disbelives the existance of God.

An atheist is...
1. Someone who acknowledges science, evidence, and all things rational instead of pure faith in a deity or deities. Instead of relying on "The Lord" to improve their lives, an atheist would be the best he or she can be.

a. The relationship between Christians and Atheists:

Some Christians attempt to verbally attack or convert Atheists and vice versa. Both have their extremists and their everyday average joe citizens who do not intervene with the lives of the opposite.

The logical thing to do in a situation like this where some of both factions are at verbal war is to simply leave the opposite alone. The saying "If you have nothing good to say, don't say it" comes into play here.

A highly disputed term that can have any number of meanings.

The following are three colloquial definitions as understood and used by the average American:
1) Someone who believes that there is no God/Gods
2) That asshole who spends all of his time arguing with or scoffing at Christians about their beliefs.
3) A socially-depraved menace to society bent on burning our churches and brainwashing our children into joining their cult which is really based on worshiping Satan and may be headed by the Jews in their attempt to control the world's money and media in order to enslave us all... (I can go on)

But it's only fair to explain atheism as defined by atheists. After all, they are the ones who identify with the term. So what do THEY believe?

Generally, there are two strains of atheism, as used by atheists:
1. "Strong" atheism- The belief that there are no Gods
2. "Weak" atheism- The lack of belief in Gods

The vast majority of atheists fall into category 2. You're hard-pressed to find an atheist who is absolutely certain that there is no God.

There is a confusion about the terms "agnosticism" and "atheism" and it's important to make the distinction clear.

Agnosticism is a position concerning knowledge of Gods. Agnostics either:
1) believe that there is no way to know for certain whether or not there are Gods
2) are undecided on the issue because they currently lack sufficient evidence

Meanwhile, atheism/theism are positions concerning what you do and do not believe regardless of any claims to knowledge. Thus, fusions between the two are likely:

Agnostic atheist- I do not believe in any Gods because 1) or 2)
Agnostic theist- I believe despite 1) or 2) for any number of reasons (fear of hell, hope, comfort, feeling that there must be some great power/first cause, etc.)

Most self-proclaimed "agnostics" are also atheists. It's very common to hear someone who calls him/herself an agnostic say,
"I don't know whether or not there is a God, so I am neither a theist nor an atheist". But like the second strain of atheism, they do NOT have belief in any Gods. If they did believe, then they wouldn't be undecided! Thus, they are undecided and without belief (agnostic atheist). In much the same way, you can say that all infants and animals are also agnostic atheists!

Now, I say this is true for MOST self-proclaimed agnostics because I have yet to hear someone call him/herself an agnostic AND claim to believe in a God. This is because most self-proclaimed agnostics think of agnosticism as a third-choice between atheism and theism. I'm of the personal opinion that this is largely due to the many negative connotations surrounding the term "atheist" (see colloquial definitions above)

I apologize for the obscene length of this definition (inb4 tl;dr!), so I won't go into detail concerning this next point:
Atheism is NOT a religion. For the same reason, theism is also not a religion. You need more than mere belief/disbelief in a God(s) to be aptly identified as a religion.