Click here for a good article on transposing instruments.
The standard clarinet is a B-flat transposing instrument. Most instruments are "C instruments", so when they play a note written as a "C" in their music, it sounds like a C on the piano. On a clarinet, though, when they play a note written as "C" in their music, it sounds like a B flat on the piano.
So... any note written for a Bb clarinet should be transposed down a whole step to understand what the real note is. You can do the same thing with key signatures. So in your question -- if the clarinet part is in the key of B flat, you'd transpose that down a whole step to get the real key, A flat.
