Why have a seperate system for flaps? Which is alternate flaps
Both systems power the flight controls, with manual reversion as a backup if both fail (except for the rudder -- that's backed up by the standby hydraulic system).
The A system powers the landing gear for retraction, extension, and nose wheel steering. The backup is a mechanical release to drop the gear if the A-system fails; there is no backup to retract the landing gear without the A system. (For those who know what the LGTU is, I'm not forgetting about it, but that's more detail than this question is asking for.) Nosewheel steering can be selected to use the B system, starting with the Next Gen 737's; before that, it wasn't backed up & you'd stop straight ahead on the runway & be towed to the gate in the event of A-system failure.
The B system powers the flaps and leading edge devices, with an electric backup that can extend and retract the flaps, and can (only) extend the leading edge devices.
Both systems can power the wheel brakes, and if both fail there is a hydraulic accumulator that gives enough brake applications that you can stop straight ahead.
There are more details, but as a big-picture overview, that's what powers what & how each is backed up.