"First of all man exists, turns up, appears on the scene, and only afterward, defines himself."—Jean-Paul Sartre
"There is nothing with which every man is so afraid as getting to know how enormously much he is capable of doing and becoming."—Soren Kierkegaard, father of existentialism
Existentialism is the response to the soul-crushingly fatalistic, Darkness-Induced Audience Apathy-fostering worldview of Nihilism. For an Existentialist, sure the "meaning of life" is brutally Deconstructed as not being able to exist objectively and all our hopes are a cruel illusion, we Humans Are Flawed and there's nothing we can do about it, but then again each individual has the choice to make the most meaningful out of each hour of our lives — those who choose to spend it being bored, or following others, or wangsting endlessly are wasting it.
Existentialism often advocates individuality and involves things like Be Yourself, Desperately Looking for a Purpose In Life, I Am What I Am, living out your Goal in Life, Earn Your Happy Ending, and sometimes moments of You Are Not Alone. This gives a world-of-cardboard/Patrick Stewart Speech to the nihilists and reconstructs the "meaning in life" concept.
The term Existential Angst is even coined to describe the sudden feeling of Quicksand Box it gave them, especially if they had just abandoned the Freedom From Choice provided by both religion and social peer pressure.
Existentialist character types include The Anti-Nihilist and The Ubermensch (the extreme Blue and Orange Morality version). The Knight in Sour Armor or Determined Defeatist have some elements of this.
While existential motifs are Older Than You Think, Søren Kierkegaard, Fyodor Dostoevsky and Friedrich Nietzsche foreshadowed in the 19th century some of what would be the defining characteristics of the philosophy, although they didn't know each other and the philosophy was unnamed. The term "existentialism" seems to have been coined by the French philosopher Gabriel Marcel. It gained popularity in the early 1940s around the time of the Modernist movement (amidst scientific discoveries of large and downright weird things out there, which inspired Lovecraftian Fiction, and of course the horrors of World War Two), when Jean-Paul Sartre codified existential philosophy with three words: "Existence precedes essence." It was the reverse of most previous philosophical thought, which held that the essence (soul, purpose, meaning) of a thing came first.
You'll find that many of the people held up as examples of existentialism indignantly claimed that they weren't -- probably a side-effect of the fact that noncomformity is one of the school's main tenets ("Once you label me, you negate me" is a famous line of Kierkegaard's).