Atheists generally accept we can’t prove or disprove the existence of God – basically, given our contingency of knowledge we can’t really ‘prove’ anything without relying on premises that themselves aren’t proven.
The hypothesis that there is a God – some agent that we are not aware of, that might have created the universe, that might interact with us in some as yet unknown way – is a reasonable hypothesis. There’s just no evidence to support the hypothesis.
So, shouldn’t the term ‘agnostic’ be used instead?
Well, the total lack of evidence for the existence of God, and the more than adequate evidence for natural explanations for what is often attributed to God, leaves little room for supposing there is a God.
Similarly, we have no evidence for many other gods of old, or of the efficacy of astrology, homeopathy, etc.
So, to all intents and purposes the label ‘atheist’ fits better than that of ‘agnostic’, given that the latter label is usually reserved for those that suspect there might be a God, but who just remain less convinced than a theist.
This form of atheism is usually termed weak or implicit atheism.
There’s also strong or explicit atheism. This atheist explicitly denies the existence of gods. This is a strong claim, and should require supporting evidence. Sometimes an atheist may give the impression of being this type of atheist, when in fact they are not. If in doubt, ask.
Though Atheism ends in -ism, it isn’t referring to a specific doctrine, and so shouldn’t be confused with being a religion, a philosophy, or a belief system – though it could be part of any one of these. There might be a religion which doesn’t have any gods, and therefore might be an ‘atheist’ religion – though then one should ask why it’s being called a religion and not an ideology or some other appropriate name.
When I refer to myself as an atheist I usually mean that this is a point of view regarding gods – all gods, which is a conclusion reached as a consequence of my understanding of what we can and can’t know (see Contingency of Knowledge and Human Fallibility), and what evidence there is or isn’t to support the hypothesis that there is a God (or gods).
Update: Agnostic-Atheist. Interesting, but there still seems room for a plain old agnostic: someone who is interested, but is completely undecided.