Answer:
World War II designation for particular plays of absurdist fiction written by a number of primarily European playwrights in the late 1950s. It is also a term for the style of theatre the plays represent. The plays focus largely on ideas of existentialism and express what happens when human existence lacks meaning or purpose and communication breaks down. The structure of the plays is typically a round shape, with the finishing point the same as the starting point. Logical construction and argument give way to irrational and illogical speech and to the ultimate conclusion—silence. The Theatre of the Absurd is a term that some people find very helpful and others find really frustrating and reductive. The term was first used by Martin Esslin to describe post-WWII dramatic literature that contained (in his view) Existential themes and that played heavily with the Modernist form. Specifically, these plays use themes that seemed in line with Albert Camus' definition of "the absurd" in his work The Myth of Sisyphus. Camus defines the absurd as the search for meaning in a world devoid of truth, God, and absolute morality. So, in experiencing a work of the Absurdist tradition (according to Esslin) the audience should feel this same emptiness. Esslin points to Beckett's Waiting for Godot as an example of a work of the Absurd. I doubt this will be the most astute analysis, but here is a brief list of absurdist features and how they can be seen in Godot. (Please see Martin Esslin's work "The Theatre of the Absurd" for a more in-depth and accurate look).
• Plot: Waiting for Godot is a play that is about...well...waiting. Or a play about nothing if you prefer. Explaining the plot to a play like Godot, is a little like explaining a dream to a friend: it makes sense in the moment, but once you put it into words, the reason and logic all falls apart. Plot structure also seems to fall apart with Absurdits works. With Godot, the second act seems to resemble the first act to and it's not easy to point to a clear climax. This is actually fairly key, and Esslin discusses circular plot structures as being a main feature of many (but not all) absurdist works.
• Theme: The characters suffer, and wait, and talk endlessly on pointless things. They fail to find meaning for their suffering, and the audience is left with as much a sense of emptiness as the characters. But still there's that dismal sense of hope, "I must go on. I can't go on. I'll go on" Beckett writes. Esslin points to a successful performance at an American prison in the 50s. This group of uneducated prisoners instantly understood a work that was esoteric to so many others. This might be that these prisoners were living the theme of the play: total monotony but sad desperate hope in the face of despair.
• Language: One distinguishing characteristic of the absurdest use of language is a lapse into illogical and what one of my acting professors liked to call "altered states of consciousness." This is perhaps best illustrated by Lucky's speech in Godot. (A speech about something, we're just not sure what.) These moments of total illogic (as seen here) are actually punctuated by moments of naturalistic dialogue, perhaps furthering the absurd affect.