Most importantly Mode S allows the radar to interrogate each aircraft selectively (using the aircraft's unique address) and can therefore provide useful ranging on the ground.
Mode A/C is non selective so everyone in the radar-beam replies - and at ranges commensurate with the size of an airport that means massive garble.
Just to clarify on the comment from Ian W.
Mode S (known as extended squitter - ES)
Mode S is
not Extended Squitter.
Extended Squitter is a sub-function of Mode S which carries ADS-B data. A Mode S transponder will 'squitter' whether or not it is seen by a radar. If it is seen by a radar it will also 'reply' to the radar interrogations.