What is the difference between having a tethered and untethered charger?

On a tethered charger, the cable that connects to your car is permanently attached to the charging station. With untethered chargers, the cable can be disconnected from both ends (the car and the charger). 
Untethered cables can be useful to leave in your car to use at public charging stations, if your vehicle didn't come with one.
AGL sell home chargers and have both tethered and untethered options.