The home note and scale a piece is built around. Major keys tend to sound bright; minor keys, darker.
A key is the musical home base: the note the music wants to return to, and the scale that goes with it. "In D minor" tells you the home note is D and the scale is minor, which usually means a darker or more serious color. Composers move away from the home key to create tension and come back to resolve it. You do not need to hear the key to feel that tension and release.
Also seen as: key signature, major key, minor key