Function
The controllers for the PS2 are specifically designed to work with the gaming system. They control each feature of the PS2 and without them the PS2 cannot function.
Significance
Since the PS2 doesn't use USB ports or other universal connection methods, you must use only Playstation approved and licensed controllers.
Considerations
Playstation 3 controllers utilize the USB interface in order to connect to a console. Because they don't have PS2-style connection ports they are not backward compatible with the PS2.