Existentialism is a relatively broad movement, like empiricism or rationalism, that has a rich and wide-ranging history, so much so that people debate what is and isn’t existential. But here’s a brief history of the roots:
Sartre coined the phrase “existence precedes essence”, which has since been a rallying cry for existentialists. That is, there is no essential quality to being a human that we all share. There is no ‘essence of humanity’ we just are: from there you have to make yourself.
Existentialism is concerned with what it means to be, and it’s fiercely individualized. The central theme running through the whole movement is that there is no ‘universal’ human experience. It started out with Nietzsche and Kierkegaard, who don’t and do believe in God respectively, and who are equally vehement about the question.
So Kierkegaard takes this individuality to mean that we each have to relate to God on a personal level, that there is no universal set of rules or principles for salvation - we have to work it out with “fear and trembling”-which comes straight from Phillipians 2:12 and was the name of one of his major theological treatises. Nietzsche, on the other hand, thought that the Übermensch would forge his own way with brazen disregard for any imposed morality, any code that tried to tell him how to live; he made his own life because he was the only one living it.
Camus rejected any attempt to make meaning and he thought the Übermensch was a ridiculous project. Nietzsche thought we should breed an Übermensch, Camus was like, “Bro, what a waste of time, why even bother? SPOILER ALERT: The Übermensch is going to die too. And then his life will be as meaningless as everyone else’s.”
Since then, existentialists both theistic and atheistic have tried to figure out how to best represent our individuality. But this, first and foremost, is the requirement for existentialism—a rejection of any sort of universal definition of man beyond his need to make himself.