The parts compose the whole. The whole comprises its parts. That's a useful pair of words, but unfortunately "comprise" has come to be used as a sort of redundant synonym for "compose."
In fact, nowadays one probably encounters the verb comprise most often in the nonsensical expression "is comprised of." A few months ago on some NPR program or other I heard someone argue that "is comprised of" has become such a commonplace phrase that it is now acceptable simply as a matter of established usage.
I admit I'm often sympathetic to such arguments. For example, I've never been a fan of the AP Style Guide's advice (at least in editions of years past) that it's incorrect to say "she graduated" or "she graduated from" college or high school on the ground that schools graduate students rather than the other way around. It was necessary, the AP said, to write, "she was graduated from" the institution in question. In fact, "She graduated college" is long-established and unambiguous and I see no reason to insist on "was graduated."
On the other hand, preserving the useful separate meanings of comprise and compose strikes me as a battle worth fighting, uphill though it might be. For one thing, most of the time when people say "is comprised of" they could simply say "comprises." Or if they for some reason wanted a wordier construction they could say "is composed of" or "is made up of." They could also say "constitutes." There's no shortage of ways to say the same thing, what does adding "is comprised of" to the set of possibilities get you?
OK, I suppose there's the fact that saying "is comprised of" annoys pedants like me, which may be fun...