For most installations of electric fence chargers, the ground connection is required for the shock to be effective. If the Fence and the Ground terminals of the fence charger are connected to different strands of the fence then, the ground connection would not be required to get the shock. In this case the full shock of the fence charger would be felt between the different strands of the fence but not necessarily from the fence to ground. This method is primarily used when the ground is very dry (desert conditions).
For the more normal electric fence charger installation, the ground terminal is connected to one or more ground rods. The number of ground rods required for the installation is determined by the power of the charger and by the condition of the soil. The pulse from the fence charger goes out onto the fence and must complete the circuit by returning through the animal and into the ground and then traveling in the moisture in the soil and back up the ground rod and to the ground terminal of the fence charger. If this is a poor circuit then the shock will be weak. As a rule of thumb, one ground rod is needed plus one additional ground rod for each 4 joules of output power (ex. for a 8 joule output charger you would want 3 ground rods). These ground rods should be 6 to 8 feet deep. Ground rods are normally galvanized and are sufficient but copper rods are better. They should be spaced at least 10 feet apart and should be connected with a good conductor ( at least 12 ga. copper or 12.5 ga fence wire) with clamped connections to the Ground terminal of the fence charger. It is preferable to use a good antioxidant paste on the connections.
The ground rod connection is not only needed to get a good shock but is also required for lightning protection. If you purchase a fence charger that has good lightning protection circuits inside, then the method of lightning protection used is normally to short the energy from the lightning to the ground rods to protect the rest of the circuitry from damage, bypassing the rest of the circuit boards and sometimes blowing a fuse. If the fuse is available to the customer then often an inexpensive fuse replacement will save damage on more expensive circuit boards and the transformer (the most expensive part and the heart of the fence charger).
I hope this is helpful in explaining the importance of the ground rods and their connection to the fence charger.