SO WHAT EXACTLY IS TRANSPOSITION?
If you wanted to play a duet on your Bb trumpet with a flutist, a ‘C’ instrument, you’d quickly find that you’re not playing the same notes. In fact, you’d be a whole step apart. The resulting sound might be strange, perhaps even interesting, but not correct. One of you would need to transpose. Either the flute player would have to read each written note a whole step down, or the trumpet player a whole step up.
The same would be true if you walked up to a piano and tried to match each note. A concert C on the piano is the same as a written D for the Bb trumpet, and vice versa. To put it simply, if you play a written C on your trumpet music, you’re actually playing a concert Bb.