What is existentialism?

Basically it's the philosophy that we define our selves by the choices we make in life and are not defined by a higher force.
I think thats as basic as I can explain it...

To understand existentialism, it's best to start with atheism. If there's no God, where does the meaning of our lives come from?

The existentialist's answer is essentially "there's no meaning until YOU define it"... i.e. you are responsible for self-generating a meaningful life. Thus anybody who's looking "out there" trying to find the meaning of life will be hopelessly lost, they have to look in the mirror, so to speak.

Of course, I can't just answer the question without preaching: while I agree with the personal-responsibility emphasis, the existentialists are wrong. Why? Because the philosophy depends on a false premise, hidden deep within it's bowels -- it depends on the notion that a human being is a separate unit of being -- separate from others, from humanity, and from life as a whole. There's no evidence for this premise, and in fact it's quite easy to challenge and disprove, but it goes entirely unchallenged much of the time.

The existentialists bought it, without realizing that it was in the philosophical package they were born into, and wove their explanation of life with that damaged thread.

But they do write well, at least.

Like B. Krayzee said - also that life doesn't come pre-loaded with meaning. We create our own meaning.

According to Existentialism:
(1) Existence is always particular and individual—always my existence, your existence, his existence.
(2) Existence is primarily the problem of existence (i.e., of its mode of being); it is, therefore, also the investigation of the meaning of Being.
(3) This investigation is continually faced with diverse possibilities

It is a philosophical movement oriented toward two major themes, the analysis of human existence and the centrality of human choice. Existentialism's chief theoretical energies are thus devoted to questions about ontology and decision. It traces its roots to the writings of Søren Kierkegaard and Friedrich Nietzsche. As a philosophy of human existence, existentialism found its best 20th-century exponent in Karl Jaspers; as a philosophy of human decision, its foremost representative was Jean-Paul Sartre. Sartre finds the essence of human existence in freedom—in the duty of self-determination and the freedom of choice—and therefore spends much time describing the human tendency toward “bad faith,” reflected in humanity's perverse attempts to deny its own responsibility and flee from the truth of its inescapable freedom.

Also described as any of the various philosophies dating from about 1930 that have in common an interpretation of human existence in the world that stresses its concreteness and its problematic character. Both the ontology and manner of human existence are of concern to Existentialism.

As Jean-Paul Sartre wrote, the most fundamental premise of existentialism is that "existence precedes essence", that is, we were here before we had a reason to be here. I am myself a Christian existentialist, much like Soren Kierkegaard, but much of Sartre's ideas hold true for my beliefs as well. Basically, unlike a paper cutter or pencil, which were imagined and had a plan and purpose before they were created, we were created with no plan. What the other answers have described was the watered down version of John Locke adopted by James Madison called the blank slate theory, that humans are born as blank slates. Existentialism has more in-depth issues. One is anguish, the idea that the choices we make for ourselves, since we would never logically choose evil for ourselves, are the choices we make for all of humanity. In this sense, Stableboy, humanity is linked, for we all affect each other. The other premises Sartre mentions are based on atheism, a theory to which I do not ascribe myself. Stableboy also nailed it with personal responsibility, as Sartre said "We are alone, with no excuses." This means that we cannot blame fate or other people or anything for who we are or even THAT we are, as everything we do is by our own personal choice. Along those lines, our beliefs are also our choices, and cannot be wrong in our eyes, nor is there a power capable of deeming such beliefs wrong. Hence, if you do not believe the theories of existentialism, that is your choice.

If you want a very well-written and rather short explanation of existentialism, find Sartre's "Existentialism and Human Emotions", it's a good primer especially if you just want to learn about existentialism, as it was written as an explanation for non-existentialists.