A grouping of things, abstract or concrete, whose every member is also a member of a larger grouping. Good examples would be:

• Volvos as a subset of automobiles
• Automobiles as a subset of vehicles
• Asia as a subset of big haired eighties bands
• Roguelike games as a subset of computer games

. . . and other such cinnamony goodness.

A band made up of all the ex-The Presidents of the United States Of America and fellow Seattleite Sir Mix-A-Lot. Very interesting, since it combines the elements of both without diminishing either part of the band. The music is goofy, the lyrics are funny and often sexist and crass as hell. They are, apparently, working on an album to come out some time this year. Don't quote me on that, though...

In mathematics:
Let A and B be sets
A is a subset of B if every element belonging to A also belongs to B.
Example:
Let A = {1,2,3} and B = {1,2,3,4,5,6,7,8} A is a subset of B because every element that belongs to A also belongs to B. see also: proper subset

In the set theory branch of mathematics,

The set A is said to be a subset of B if and only if every element on A is also an element of B.

or

The set A is a subset of the set B (denoted: A ⊆ B) iff
∀x ( x∈A → x∈B )

(In English, that's "for all x, 'x is an element of A' implies 'x is an element of B'")