Many people confuse or equate the terms, but there is a definite difference between the two.
An atheist, on the one hand, believes that there is no God. Etymologically, the word means “not, or no God.” In the atheist camp you can have a wide variety of reasons for their denial as well as differing levels of certainty. Some will deny emphatically that there is a God and claim to have “proof” of God’s non-existence. Other’s will simply say they do not believe there is a God though they could not prove God does not exist. The common denominator is that they do not believe in God.
Agnosticism is not a belief system as atheism is; rather, it is a theory of knowledge. Etymologically, it means, “not, or no knowledge.” An agnostic is someone who believes human beings simply cannot know anything metaphysical or beyond the physical realm; therefore, they cannot know whether things like spirit, angels or God exist at all.
Contrary to popular belief all agnostics are not atheists. There are theistic agnostics–fideists, for example–who believe in God but do not believe that their understanding of God is knowable by natural means. Vatican I declared this belief to be contrary to the Catholic Faith in Session 3, Canons, chapter 2, canon 1:
If anyone says that the one, true God, our creator and lord, cannot be known with certainty from the things that have been made, by the natural light of human reason: let him be anathema.