"Bittersweet" is an oxymoron. An oxymoron is a two-word paradox, or something which appears to be a contradiction, but is actually possible. Other examples include "living dead", "darkly lit", "sweet sorrow", etc. In each of these, the concept seems to be impossible (how can something which causes sorrow or sadness also be sweet or pleasurable?), but can actually exist.
The Enotes Guide to Literary Terms states the etymology as follows:
The term comes from the Greek oxumoros, meaning pointedly foolish which was formed by combining oxus, meaning sharp, and moros, meaning foolish.
An oxymoron can be a effective way to state a paradox concisely, & thus point out discrepancies or emphasize a particular point.
Like the previous post, "bitter sweet" is an oxymoron. It comes from two Greek words, meaning sharp and dull. So, even from the word itself, you are able to get at the definition of the word.
Oxymorons are great to use in literature, because it makes the reader think. It is similar to a paradox in some ways. On the surface, it does not make sense at all, but with some more reflection, usually a great truth is unlocked with wit and cleverness. Moreover, most of life is filled with oxymorons. For instance, no one is consistent. Everyone is a walking contradiction. In part this is what makes life interesting.
A nice oxymoron is "silent whispers." If we expand this idea, we can say apply it also the conceptual things.