In Music theory, the key is the tonal center of a piece. It is designated by a note name (the tonic), such as C, and can be either in major or minor mode. Other modes are also possible, for example: dorian, phrygian, lydian, but most popular music uses either the major (Ionian) and minor (aeolian) modes. 18th and 19th century serious music also tended to focus on these tho modes.

The major mode has half-steps between scale steps 3 and 4 and 7 and 8. The natural minor mode has half-steps between 2 and 3 and 5 and 6. You can see an online video that teaches the structure of the major scale at:

   http://www.ilovemusic.com/improvise_music_e-flat.htm

What a key designates to a performer is the scale in which all the diatonic notes of the piece lie. This is slightly more complicated in a minor key, because the pitch of the sixth and seventh scale degrees in a minor key can change depending on their harmonic context. The primary key of a piece of music is indicated at the beginning of the piece with a key signature.

A piece may change key at some point. This is called modulation. Modulation is sometimes done by just starting in the new key with no preparation - this kind of key change is common in various kinds of popular music, when a sudden change to a key a whole tone higher is a quite frequently heard device at the end of a song. In classical music, however, a "smoother" kind of key change is more usual -- this kind of key change is called modulation.

You can find a thorough tutorial on modulation at:

    http://www.ilovemusic.com/modulation.htm 

Certain musical instruments are sometimes said to play in a certain key, or have their music written in a certain key. Instruments which do not play in the key of C are known as transposing instruments. The most common kind of clarinet, for example, is said to play in the key of B flat. This means that a scale written in C major in sheet music will actually sound as a B flat major scale when played; that is, notes sound a whole tone lower than written. Likewise, the French horn, normally in the key of F, plays notes a major fifth lower than written.

Similarly, some instruments may be said to be built in a certain key. A brass instrument built in, say, B flat, will play a fundamental note of B flat, and will be able to play notes in the harmonic series starting on B flat without using valves, fingerholes, slides or otherwise altering the length of the vibrating column of air. An instrument built in a certain key will often, but not always, have its music written in the same key (see trombone for an exception).

See also: tonality