"Existentialism" is a subject that is very difficult to describe precisely. As we can see, it stems from the word "existence", but what of existence? What makes the theme of existence so profound? It is obvious we exist, is it not? Therefore it's not the term "existence" that is so notable. Rather, it is the relation of this term to one other term: "essence". The saying Jean-Paul Sartre uses is, "existence (that a thing is) precedes essence (what a thing is)", and that is the overlay of his branch of existentialism.
As we've determined, existence is the process whereby something comes into being. Man defines himself (his essence) through the fact that he exists. Humans are, according to Sartre, "condemned to be free". For without an absolute god or a pre-existing universal definition, they are free to create their own definition through their actions and choices. However, with such inherent freedom comes the burden of responsibility for their decisions and actions. This is why Sartre identifies such freedom as a condemnation. We must exist before we have a purpose, and consequently, we must establish a purpose for ourselves once we are placed on this earth. This gives us a reason to exist. The problem we face is: what purpose do we choose for ourselves? That is part of the responsibility we must assume.
According Sartre, God was a human creation, developed in order to give man a purpose. This idea was actually referenced to by Friedrich Nietzsche in his famous (or infamous) statement, "God is dead", made in his work Also Sprach Zarathustra. Nietzsche asks, "What? Is man merely a mistake of God's? Or God merely a mistake of man's?" Sartre implies that the latter is more likely, though he doesn't refer to it as a mistake. According to Sartre, God was a necessary development of man for the purpose of establishing an ethical code to live by. But the idea of God was conceived in "bad faith".