The word transposition comes from Latin and means movement, passage. In music it means a transfer of a particular musical text into another tone pitch, higher or lower than written, ie. from written tonality into proper one.
Note text can be transposed in writing, but in practice it is necessary that a performer is able to transpose a particular part in the new tonality while playing.
This practice of transposition is particularly needed to orchestra clarinetists, because they usually play on the B♭ (in B) clarinet but a part of a composition can be written for the C (in C) or A (in A) clarinet.
Taken from my book