Although it is never stated in the play that they were tramps, Vladimir and Estragon wear bowlers and resemble tramp-like characters played by Charlie Chaplin, Buster Keaton, or even Laurel and Hardy. This underscores the tragicomic nature of the characters. In these cases, the tramp is in a situation where he is at the mercy of external forces and his struggle through those forces is often comedic or just downright ridiculous. Of course, the characters in "Waiting for Godot" are in a dark and seemingly more absurd situation than those in comedies. In performances, they were also usually dressed in drab clothing, in front of drab scenery (sans the tree), and since nothing happens, they are sort of 'part of the scenery' - they blend in.
In the case of tramps, Becket may have chosen the similarities to Chaplin (and others) purposefully, but he might not have. He was always evasive about commenting on reasons for the choices, usually stating idiosyncratic whims as his reasons. For example, he claims that any relation between Godot and God is either misconstrued or something he did unconsciously.
A tramp is often described as a homeless person, a wanderer = someone on the outskirts, not part of the ongoing progression of society. People get a sense of meaning and importance being part of historical development. Think of the tramps in this play as shipwrecked. They wait for something to happen, perhaps even to be saved. Religious allegories abound here, but more importantly, the tramps are forced to imagine a universe for themselves: otherwise, they do nothing. Being detached from society (because they are tramps and are waiting), they are not part of any societal optimism (the basic idea of progress in society is that things steadily improve - agreements and disagreements will abound here as well.) Therefore, the tramps must consider their own place in the universe. In other words, if they are there alone, what can they do that has any significance, besides simply waiting?
The tramp (wanderer) must always think, "Where am I going? When will the wandering end?" So, he is more subject to philosophical introspection (as dark as it can be at times) than someone who is caught up in the fast-paced day-to-day life that most people are, with work, family, and so on. It is interesting, tragic and comic, because they literally must entertain themselves while waiting. They are the source of their own amusement.