The water lines of the house are a hydraulic system. Without the tank the instant you cracked a water valve the pressure of the system would drop to zero. There is a pressure switch that starts the pump. The bladder tank is an accumulator that puts an air cushion in the line which reduces the number of pump start / stops. The purpose of the bladder is to keep the air in the tank from diffusing into the water and coming out of the faucet.
edit: and as BB2k said: the bladder tank reduces pressure fluctuations at the faucet. It smoothes out the pressure spikes from the pump starting and stopping. The system will not work without the tank -the pump would start and stop repeatedly as the pressure instantly goes high and low!
