The Difference

THAT is a defining (sometimes called restrictive) pronoun.
WHICH is the nondefining (nonrestrictive) pronoun.

Examples:

The lawnmower that is broken is in the garage.
     (tells which lawnmower is in the garage--the broken one)

The lawnmower, which is broken, is in the garage.
     (adds a fact about the lawnmower being talked about)

It's a bit confusing at first, but remember this rule: THAT means "which one."