First off, what is the title, exactly? You may have seen it as Notes from the Underground, as we refer to it on Shmoop, or Notes from Underground, or even Letters from the Underworld (someone was feeling creative that day). This is all the fault of translation; since the work was originally written is Russian, it quite fittingly has a Russian title. Translations are never exact, so you end up with a variety of titles to choose from . Notes from Underground is the most literal translation; we refer to it as Notes from the Underground because Shmoop uses the Constance Garnett translation by that name.
On the surface, Notes from the Underground is a set of notes written from underground. (As you'll read in "Symbols, Imagery, and Allegory," the "underground" hovel is likely metaphorical. This guy is "underground" in the "I'm anti-social and hate the whole world" sort of way.)
But that's not all. We're dealing with Russian literature; so there's always a shout-out to other great literature somewhere. As you've likely heard by now, Notes from the Underground was in part a response to Nikolai Chernyshevsky's What Is to Be Done?. In Chernyshevsky's novel, while ranting about how great rational egoism is, one of the characters asks rhetorically, "Do you hear that, in your underground hole?"
Of course, this question didn't stay rhetorical for long, because Notes from the Underground gives an answer (In short: "You bet your fanny I hear it, and oh man, do I have a lot to say in return. You'd better have a seat.")