Comprise means to consist of or to be composed of. Compose means to make up the constituent parts of. Parts compose the whole, and the whole comprises the parts. For example, we could say that the United States comprises 50 states and that the 50 states compose the United States.
But comprise is widely used in illogical ways, mainly in phrases such as is comprised of. For example, many people would write that the United States is comprised of 50 states even though they obviously mean compose instead of comprise. This usage is so widespread that trying to stop it is probably a lost cause, and we increasingly have to turn to editorially fastidious publications to find comprise used the old way. Still, careful writers tend to avoid the mixup.
Here are a few examples of comprise used well in its traditional sense:
The development – on a site which used to comprise one large house and a tennis court – has been going on for a couple of years now. [Guardian]
Mr. Litterst said the incident management team comprised 238 Park Service employees from around the country. [New York Times]
The first is that a monetary union comprising 16 or more EU members will ultimately require a fully fledged fiscal union, or fail. [Financial Times]
The transitional government comprises members of both the ruling party and the opposition. [Washington Post]