It is when you solo in a key other than the key the piece of music is in.
E.g. soloing in the key of Db when the piece is in the key of G.
There's a reason I said Db when in G, but i'm not going to give you all the answers )
Bill Evans played 'outside' a lot. The term is generally considered a jazz term, as jazz players often play outside (try John Coltrane also, amongst many others).
E.g. soloing in the key of Db when the piece is in the key of G.
Oh, I know *some* of the answers (tritone, lydian dom, etc. )
..but I wanted to get a lively debate going; through the debate I hope more will be revealed little by little.
So to your point on 'playing outside of the key' is this the strict definition? If my piece is in C and I play the notes from G, only one note differs - the F#, so I'm only outside of the key for that one note.