Existentialism, for our purposes anyway, could be defined as the realization that nothing exists beyond the physical world surrounding us. It's the logical endpoint of The Age of Reason (no accident that one of Sartre's novels bears that title). As scientific thought advanced from the Renaissance to the modern era, there has been less and less room for traditional religion. When faith is replaced by empiricism, it becomes obvious that there's no God, let alone a heaven or a hell. That's what Nietzsche meant when he claimed, "God is dead."
While it's obviously positive to replace superstition with knowledge, it poses a terrific problem. If there is no God, then there is no reason for us to be alive beyond the accident of our births. We're here on our own until the day we die, and any action we take in our lifetimes is meaningless. When we die everything comes to an abrupt and absolute end. Except for fear of being punished by the law, there's no reason to live a good life any more than a bad one. In fact, the whole idea of a "good" life ceases to make sense. As Nietzsche remarked in Beyond Good and Evil, "There are no moral phenomena, only the moral interpretation of phenomena."
It's this dilemma, and little else, that has kept the major Western religions alive into the twenty-first century -- without a belief in a higher power, life would have no point for their adherents. Why even bother to get out of bed in the morning?
But this is only a problem for Western religions, which alone has sought to place God in time and space. Their beliefs hold that God is an actual entity who has acted in real (historical) time. There are those fundamentalists who believe they can calculate the exact age of the planet from a reading of the Bible. In their minds, religion has been moved from the realm of myth to that of fact.
In Asian thought, the idea of a God overseeing creation has never taken hold. Rather, in Buddhism, the goal is not to act as a good person for reward in the afterlife but to perform good acts, throught the eightfold path, in order to bring out the enlightened being dormant within. In that sense, Eastern philosophy is mre mystical than it is eschatological. There is no need for any belief in life after death. Nirvana is a state of mind, not a place.
I read once -- it may have been in one of Joseph Campbell's books -- that the difference between the Hinayana and Mahayana schools of Buddhism is this: in the former, people realize they are traveling on a boat that's headed nowhere and they freak out and start wailing how terrible it is; in the latter, people realize they are traveling on a boat that's headed nowhere and think, "What a blast. Let's party."
Buddhism accepts the inherent absurdity of life. It's only when the total meaninglessness of existence has been accepted that one is free to enjoy life.