Key
A key is a tonic and a mode together: G major, for instance, is the major scale and chords whose home note is G. The key signature, right after the clef, tells you the key.
The name of a key says two things: which note is the tonic, and whether the mode is major or minor. C major, G major, F major, A minor. On European scores you will also see German letter names: a capital letter with dur for major, a small letter with moll for minor – C-dur, G-dur, F-dur, a-moll, e-moll, d-moll.
Each key has its own key signature. No sharps or flats: C major or A minor. One sharp (F♯): G major or E minor. One flat (B♭): F major or D minor. A major and a minor key with the same signature are called relative keys; the tonic – the note the piece comes home to – tells you which of the two you are in.
The same tune can be played in another key – that is transposing: the steps stay the same, only the starting note and the key signature change.
What it sounds like
A key is heard as a sense of home: listening to a piece, you feel which note is the tonic even without seeing the music. A major key sounds bright, a minor key darker.
Where it is taught: the studio’s interactive textbook, chapter 7, “G and F major: key signatures” and chapter 8, “Minor: A minor and relative keys”.