Wikipedia
A transposing instrument is a musical instrument whose music is notated at a pitch different from the pitch that actually sounds ( concert pitch). Playing a written C on a transposing instrument produces a pitch other than C, and that pitch identifies the interval of transposition when describing the instrument. For example, a written C on a B clarinet sounds a concert B.
Rather than a property of the instrument, the transposition is a convention of music notation—however, instruments whose music is typically notated in this way are called transposing instruments. As transposing instruments is a notation convention, the issue of transposition is mainly an issue for genres of music which use sheet music, such as classical music and jazz (while jazz is an improvisation-based music, professional players are still expected to be able to read lead sheets and big band sheet music). For some instruments (e.g., the piccolo or the double bass), the sounding pitch is still a C, but in a different octave; these instruments are said to transpose "at the octave".