Their purpose is one or all of three:
1. Impedance matching
2. Balanced(3-conductor) to Unbalanced(2-conductor) conversion
3. Earth Ground Lift/Connect
For most uses it converts an unbalanced, high impedance signal (the kind of signal generated by most pickups and dynamic mics) into a balanced, low impedance signal (the kind of signal required by most mixers and pre-amp inputs). It also isolates the output signal from the input signal, so it can be used to cure ground loop problems in other parts of the signal chain (like between a mixer output and a power amplifier input).
-JV
I took this explanation from another site and modified it slightly. I guess I'm just lazy!