How is the word absurd used in relation to literature?

Well, in literature, the Word "absurd" is most commonly associated with a worldview called "Existentialism." Existentialists, such as Franz Kafka (The Metamorphosis) and Albert Camus (The Stranger) don't believe in God, instead choosing to believe that life is meaningless and bleak. To them, the violence of the world doesn't make sense, and they feel alienated from everything.

There is also a theatre of the absurd - again with mainly European dramatists like Ionesco and Samuel Beckett playing leading roles. Waiting for Godot is a key work.

It was quite a major influence in the 1960s.

If you read anything by an existentialist, you'll immediately see the relationship. Go to the link for a very short story by Kafka.