Three I can think of:
1) Reduce injury to palms when you fall off. Having come off again today for no apparent reason, I find this very important. Means you can hold pens, put dressings on rest of body, type posts in cycle chat, and most importantly, still ride the bike. Road rashed palms are no fun.
2) Padding reduces vibrations and helps prevent/delay nerve tingling and so on on long rides, as well as cumulative damage.
3) Provides a handy piece of material for wiping snot, spit, dribbled drink, splatted insects etc, some even having toweling bits on them for this. Perhaps the least important but most frequently useful.
Hope that helps