Sending line level audio signals over CAT5 cable only works for extremely short distances. There comes a point where the noise becomes irritating and the signal becomes quiet (certainly a problem with about 20m of cabling).
The transformer converts the signal from unbalanced (i.e. relative to ground) into a balanced signal (i.e. inverted waveform down each wire). The same circuit is applied in reverse at the other end of the stretch of CAT5. This cut the noise to inaudible levels.