There is, unfortunately, some disagreement about the definition of atheism. It is interesting to note that most of that disagreement comes from theists - atheists themselves tend to agree on what atheism means. Christians in particular dispute the definition used by atheists and insist that atheism means something very different.
The broader, and more common, understanding of atheism among atheists is quite simply "not believing in any gods." No claims or denials are made - an atheist is just a person who does not happen to be a theist. Sometimes this broader understanding is called "weak" or "implicit" atheism. Most good, complete dictionaries readily support this.
There also exists a narrower sort of atheism, sometimes called "strong" or "explicit" atheism. With this type, the atheist explicitly denies the existence of any gods making a strong claim which will deserve support at some point. Some atheists do this and others may do this with regards to certain specific gods but not with others. Thus, a person may lack belief in one god, but deny the existence of another god.
Below are links to a variety of references pages to help understand how atheism is defined and why atheists define it the way they do.
Definition of Atheism:
What is Atheism?
Explanation of the "strong" and "weak" senses of atheism and why the latter, weak atheism, is both broad in what it means and common in how it is applied. Most atheists you meet will probably be weak atheists, not strong atheists.
A look at how standard dictionaries have defined atheism, theism, agnosticism, and other related terms. Included are definitions from dictionaries from the early part of the 20th century down through the modern Oxford English Dictionary.
When debating atheism online, one of the most common resources used will probably be various online dictionaries. These are references which everyone has equal access to, unlike printed dictionaries which people may not have at all or may not have immediate access to (because, for example, they are currently reading/posting from work). So, what do these online sources have to say about the definition of atheism?
Specialized reference works have also provided definitions of atheism, theism, agnosticism and other related terms. Included here are entries from sociology dictionaries, encyclopedias of religion, and more.
Atheists and freethinkers have defined atheism relatively consistently over the past couple of centuries. Although a few have focused solely on the sense of "strong" atheism, many more have differentiated between "weak" and "strong" atheism. Included here are definitions of atheism from nonbelievers and freethinkers from the early 20th century and before.
A few modern atheists have also insisted on restricting atheism to just the sense of "strong" atheism, but most have not. Most have, instead, pointed out the difference between "weak" atheism and "strong" atheism, arguing that the former is the broader and more commonly found form of atheism. Included here are quotes and definitions from nonbelievers from the latter part of the 20th century and later.
Although misunderstandings about the definition of atheism have tended to come from theists, it is a fact that many theists have recognized that atheism has a broader sense than simply "denial of the existence of gods." Included here are quotes from a few of them.