The "theatre of the Absurd" is a title coined by Martin Esslin about the works of various dramatists from Beckett's time onward and absurdist playwrites are seen even today. See Theatre of the Absurd.
Although Beckett was writing his prose and drama before anyone had officially coined the name, his works are very much a part. Wikipedia defines it as "A style in which structure, plot, and characterization are disregarded or garbled in order to stress the lack of logic in nature and man’s isolation in a universe which has no (definitive) meaning or value."
Vladimir and Estragon encounter isolation and alienation from each other, other people, and the world itself as they wait for an "absent landlord," Godot, who will explain and justify everything. During the play the nature of existence and language itself is delicately considered. Check out the link for more information.
The playwrights loosely grouped under the label of the absurd attempt to convey their sense of bewilderment, anxiety, and wonder in the face of an inexplicable universe. Although the Theatre of the Absurd is often traced back to avant-garde experiments of the 1920s and 1930s, its roots, in actuality, date back much further. Absurd elements first made their appearance shortly after the rise of Greek drama, in the wild humor and buffoonery of Old Comedy and the plays of Aristophanes in particular. World War II was the catalyst that finally brought the Theatre of the Absurd to life. The global nature of this conflict and the resulting trauma of living under threat of nuclear annihilation put into stark perspective the essential precariousness of human life. Suddenly, one did not need to be an abstract thinker in order to be able to reflect upon absurdity: the experience of absurdity became part of the average person's daily existence. This makes some level of logical sense because in WWII, all traditional notions of fairness, justice, and the framework for ethical treatment of one another were completely discarded. The absurdist thinkers realized that they were using the traditional medium of the stage to convey the anything but traditional standards for human and ethical conduct. Vladimir and Estragon, the “tramps” are the central images of waiting in Beckett’s work. We can then make the assumption that these characters display the best and worst aspect of humanity, discuss elements that define existence and represent triviality, study themselves and one another, and interact with success and failure with each-other and others The characters live, love, disparage, compliment, converge, and diverge and nothing happens twice. Their hopes are never quite realized, their words never lead to action, and what is indicated is never quite actualized. Godot never arrives. This is an absurdist play in its embrace of the tragicomedy: It is tragic to witness the condition of both of the tramps, but it is also comic, from an absurdist point of view, to see that neither character does anything to change their predicament. From the Greek conception of tragedy in Aristotle, where the character gains awareness and understands their plight in order to change it, traditional art has emphasized the redemptive and consciously powerful notion of individual change. Part of what makes absurdist theatre so compelling is that it ponders and addresses the reality of what happens when characters do not undergo such an evolution. Their predicament is still dramatic, although it is tragicomic. This would be one reason why Beckett's work fits in the absurd classification.