Pressure Hose
Your washer contains an air-tight hose that runs from the body of the washer to the pressure switch. As the washer fills with water, the air that was in it is displaced, and has no way to escape but through the hose, gradually increasing the pressure on the switch.
Switch
When the pressure in the hose reaches a certain level, the pressure switch is programmed to disconnect the power to the washer's fill valve and redirect it to the timer, which causes the water to stop flowing and the washer to begin its first cycle.
Water Level Setting
Most washers allow you to set the desired water level yourself (usually low/medium/high settings). This simply changes the threshold of pressure at which the switch is told to redirect the power---the higher the threshold, the more air will have to be displaced, and the higher the water level.
Switch Problems
The pressure switch setup is relatively simple, but still contains several opportunities for failure. If the pressure hose develops a leak or is attached too loosely, air will escape and the switch may never be flipped, causing your washer to overfill. If the hose becomes clogged, the switch may consistently read the water level as too high, and never allow the washer to start. If the electrical contacts on the switch are damaged, it may be unable to redirect power directly. Examine the pressure hose and check the switch with a voltmeter if you're having water-level problems with your washer.
Valve Problems
The fill valve itself can also become clogged or damaged, causing fill problems even in a washer with a functioning hose/switch system. Check this too, and make sure you keep all parts of your washer clean and operational.