I think everyone has probably explained it better than me, but here is the Moonunit attempt to explain what cats like JohnInKansas have described so beautifully. Here goes folk(ie)s:
Disregarding whether an instrument is diatonic or chromatic...
First, if an instrument is in the key of C, we say that it plays at concert pitch. This is because when a C instrument plays the note C, you are hearing the note C!
When a Bb instrument plays the note C on their instrument, what you actually hear is the concert pitch Bb!
So if the Bb trumpets and clarinets are playing in C, the C instruments will be playing in Bb (otherwise the music is going to get painful).
If you play a Bb instrument and you want to play with your concert pitch friends, you need to transpose up a tone from their music. Likewise, if you are in concert pitch and want to play along with the Bb crew, you need to transpose down a tone from their music!
Hey ho, there I go... I hope I haven't confused things for you further Vixen.