In general, a college offers education in one specific area, while a university is a collection of colleges. When you go to a university you attend one of their colleges, such as the business college or college of engineering.
edit Differences in research focus
A university tends to maintain research requirements for its instructors and is thus usually a more "research-focused" institution. This adds a certain degree of recognition to universities and attracts a larger student body that affords them the capacity to offer higher learning options than a college can offer. Doctorate programs are more likely to be offered at universities where they have the money and ongoing research to support such programs.
edit College vs. University in the United Kingdom
In the UK, a university can award its own degrees and has a charter giving it various guarantees of independence. A college usually depends on a fully-fledged university validating its degrees, or may even be part of a university, as in Oxford or Cambridge colleges.