Historical Background

While he never identified himself as an existentialist, the 19th century philosopher Søren Kierkegaard is generally considered the founder of existentialism. The term is most closely associated with Jean Paul Sartre.
The label of existentialism is problematic as a philosophical movement for a number of reasons, most notably that the term was not even used by many philosophers(in fact some writers like Camus explicitly rejected the idea) and that there are some major disagreements about fundamental questions of politics and religion within the movement.
Existentialism was profoundly influenced by and influenced literature.
While some see existentialism as a dark philosophy that calls into question the meaning of existence, I'd argue that it presents an affirming vision, one that suggests we are responsible for our existence.

Basic Ideas of Existentialism

Existentialism does not support any of these ideas:

At its core, existentialism is the study of human existence. Professor Steven Earnshaw explains the philosophical underpinning of existentialism this way: "Existentialism is a philosophy that takes as its starting point the individual’s existence. Everything that it has to say, and everything that it believes can be said of significance — about the world we inhabit, our feelings, thoughts, knowledge, ethics — stems from this central, founding idea."
A central proposition of existentialism is that existence precedes essence, which means that the actual life of the individual is what constitutes what could be called his or her "essence" instead of there being a predetermined essence that defines what it is to be a human. Thus, the human being – through their own consciousness – creates their own values and determines a meaning to their life.

We are free to determine our lives. As Sartre puts it in his Existentialism is a Humanism: "man first of all exists, encounters himself, surges up in the world – and defines himself afterwards." Of course, the more positive, therapeutic aspect of this is also implied: A person can choose to act in a different way, and to be a good person instead of a cruel person. Here it is also clear that since man can choose to be either cruel or good, he is, in fact, neither of these things essentially.
Existentialists reject the traditional philosophical position that rationality is freedom and that passions are to be rejected. Existentialists suggest that we live best and are most ourselves when we live passionately. Kierkegaard argued that existence is a life filled with passion, self-understanding, and commitment.
We have the freedom to act with authenticity--acting as oneself, not as One acts or as one's genes or other essence require.

John Fowles, in The Aristos, wrote, “existentialism is the revolt of the individual against all those systems of thought, theories of psychology, and social and political pressures that attempt to rob him of his individuality.” In the modern age, everything from genetics to psychology seems to strip us of our agency--existentialists reject the idea that we are anything other than what we choose to make ourselves.
Some modern concepts existentialists revolt against: human nature, hormones, genetics, psychology, neurochemistry, Social Darwinism
Sartre, in Existentialism and Human Emotions, said, “existentialism’s first move is to make every man aware of what he is , and to make the full responsibility of his existence rest on him.”
Professor Robert Solomon describes existentialism like this: "The message of existentialism...is about as simple as can be. It is that every one of us, as an individual, is responsible--responsible for what we do, responsible for who we are, responsible for the way we face and deal with the world, responsible, ultimately, for the way the world is. It is, in short, the philosophy of no excuses.

Existential angst (literally "anguish" and/or "anxiety") is the negative response arising from the freedom existentialism provides. Kierkegaard’s classic example of existential angst was to describe a man standing on the edge of a high cliff or building. Along with the fear of accidentally falling, the man feels an irrational impulse to deliberately fling himself over the edge. The emotion he feels upon realizing that he has this option is angst. Kierkegaard described it as “the dizziness of freedom.”

At its core, the concept of the absurd is the conflict between the human desire/tendency to seek external meaning in life and the inability to find it.
The notion of the Absurd contains the idea that there is no meaning to be found in the world beyond what meaning we give to it. This meaninglessness also encompasses the amorality or "unfairness" of the world. This contrasts with "karmic" ways of thinking in which "bad things don't happen to good people"; to the world, metaphorically speaking, there is no such thing as a good person or a bad thing; what happens happens, and it may just as well happen to a "good" person as to a "bad" person.