the pool of water below the reactor (in this case in the torus) is designed to quench vented steam and reduce pressure in the reactor.
under normal conditions, when the reactor is pressurized, there are 2 emergency core cooling systems available to the core. The first is HPCI (high pressure coolant injection), and is an active pump meant to get water on the fuel. the second is RCIC (reactor core isolation cooling), and uses steam from the reactor to run a turbine and pump water into the core. RCIC requires only batteries....and that your suppression pool is below boiling point so it can quench the steam.
If the plant had electrical power, and they had a leak or a failure of the high pressure systems, they would vent all their steam to the suppression pool and run their low pressure core spray and low pressure coolant injection systems. the plant i'm at has 3 LPCI pumps and 1 LPCS pump. these low pressure pumps are designed for flow, not pressure, and are capable of fully filling the reactor vessel in all but the worst pipe breaks (double guillotine shear in the recirc lines). and even in the worst condition, provided you still have electrical power, the water that is lost funnels down through pipes back into the suppression pool where it can get run through heat exchangers, cooled, and pumped back into the core repeatably.
if you dont have power, the core has relief valves that automatically lift in safety mode without power if the core has too much pressure. this vents to the suppression pool. i dont know if the pool has relief valves or the containment, but you then would need to manually vent the containment to keep the pressure down enough to inject water in.
during the accident, i believe unit 2 had too much pressure build up in the core and that stopped seawater injection for a while. they had to release the pressure to allow the pumper trucks to get water back in.