Existentialism is a philosophical system that originated in the 19th century, and grew in the 20th century, that focuses on the individual striving in a seemingly meaningless universe if one rejects the biblical worldview, and how (and if) one is able to come into grips with this. Existentialism, though denying an objective meaning to life, believes that we as individuals can create our own subjective meaning of life, which differs it from nihilism which believes in neither.
There are two main types of existentialism, Atheistic Existentialism which will be the focus here, and Christian Existentialism.
Atheistic Existentialism on the other hand denies the dependency of human existence on God and views human existence as an independent and meaningless form. It asserts that we do not have fundamental attributes, such as morality or a soul, and that humans develop these attributes in a meaningless manner as their lives progress. Beyond that, existentialism means different things to different people and thus can often be the subject of debate by students of atheistic philosophy.
The name derives form one of its central concepts, the notion that a human being's "existence precedes essence."
The Danish Christian philosopher Søren Kierkegaard (1813-1855) is said to be the father of existentialism. He was born into a wealthy family which allowed him to pursue intellectual interests and distance himself from the everyday man. He is known for his pseudonymous, which was a symbol for an existing individual. He was against the philosophy of Hegel, whom he accused of bringing Christianity from something which must be lived through to a dogmatic system. He is known for his terms of 'knight of faith,' 'leap of faith,' and 'truth in subjectivity.'
Friedrich Nietzsche (1944-1990) is arguably the most well known and well read of all philosophers. His writings are easy to read and understand, mainly written in aphorisms, which he started in Human, All Too Human. He wrote books until he went insane. He is known for his ideas of the Overman, the Will to Power, the Eternal Reoccurrence, his opposition to morality, and the phrase 'God is Dead.'
The four considered the earliest existential writes are Kierkegaard, Nietzsche, Dostoyevsky, and Jean Paul Sartre. Other writers were Karl Jaspers and Martin Heidegger. The movement did not, however, develop its name or popularity until the 20th century when it was popularized by Jean Paul Sartre and Simone de Beauvoir. 
Especially Sartre says, "Existence precedes essence." He asserts that man appeared not from essence (God or an idea) but rather from nothing and then defined himself and gave essence to himself.
The writings of existentialists such as Kierkegaard,Sartre and Camus reflect an epistemology that is not only based upon the criteria of rationalism or empiricism. Theirs is an appeal to the intuitive, as reflected by Sartre’s references to the “nausea” stirred in him by the contradictions and hypocrisy in human behavior. The same appeal to the intuitive can be found in Soren Kierkegaard’s notion of dread and in Albert Camus’ reflections on universal guilt.
Existential angst (or existential crisis, existential despair), is one of the key concepts in existential philosophy, and it means the crisis that one feels when confronted with a seemingly meaningless Universe, along wth the realization that one has free will to make one's own choices. This is illustrated by one standing on the edge of a cliff, looking down, and then realizing that nothing is holding you back from jumping off. The emotions which arise from this revelation is called existential angst. 
Existential angst is much more likely to happen in gifted children. 
- Existentialism Today
- Stanford Encyclopedia of Philosophy
- Theory of the Original Human Nature - Dr. Sang Hun Lee
- A Reflection on Unification Thought, Evil, and Theodicy - Thomas J. Ward