The PS3's Blu-ray drive is notoriously slow, so in order to keep load times under several minutes, they have to dump frequently read data to the hard drive. The key here (and difference between last-gen) is that unlike xbox, the process isn't invisible as you have to wait for the install and micromanage your freespace. Unlike PS2, it isn't optional either. Games won't run if you don't install and games that don't have the install preprogrammed, won't let you. And no, you can't install to an external.
I think the reason for intsalling the games to the hdd is due to the fact that so much data is cramed onto the disk that if you played it off there it would see lag issues during reading of the disks so if it is on the hdd, the read is therefore faster and you get cleaner gameplay because of it.