Here are some examples (not necessarily designed examples) that explain the general idea of existentialist thought:
"Existence precedes essence" - Jean Paul Sartre, is probably the most famous quote that has come out of existentialism. However, it can be difficult to understand at face value. The quote is in relation to the existence of humanity. What Sartre is saying is that when considering humanity, its existence comes before any purpose that is claimed or suggested for it. He is essentially saying that there is no purpose to the existence of any human. Only that we create our own purpose based around the lives that we live. Therefore there is nothing more to life than existence. We are born, then we eventually die.