In an AWD vehicle the front and rear axles can travel different distances because of turns etc so a centre diff allows for this. If this problem was ignored, the drive line would bind up on bitumen and shafts would snap! When you lock the centre diff, it is like engaging 4WD and locking the hubs in a vehicle with part time 4WD.
So without centre Diffs and ignoring all the fancy electronic offroad features creeping in to vehicles today, the axle diff will basically send all torque to the wheel with the least load. So if you put one wheel in the air, it will spin and forward motion ceases. Now in a 4WD, With a bit of luck, the other axle might still be driving so you keep moving.
If you have axle diff locks, engaging them will lock the axle so that if one wheel turns, the other must also turn.
Having axle diff locks means you need less momentum to get over an obstacle so lower revs and more torque. You don't have to hit an obstacle hard enough to bounce over the low/no traction bits. This then permits a much more controlled approach that is less likely to damage the track or the vehicle.
Electronic traction control on an open diff attempts to do the same thing by sensing a slipping wheel on an axle and applying the brakes to that wheel only. This evens up the torque on both sides of the axle so forward motion starts again.
One point worth noting that most 4wd's including the Prado have rear limited slip Diffs. These require a higher torque differential across the axle before slippage occurs. Installing a locker replaces the LSD with an open diff so you may find yourself engaging the rear diff lock wher you could just drive on previously.
Diff locks are not usually needed on sand as the idea is to make sure you don't spin a wheel and dig in. Crossing the axles up and getting a front and back wheel spinning is not that hard to do. If possible approach an obstacle square on so both wheels have grip.