Think of an electric fence as a circle with electrical energy occupying it. The energy stays there in harmless fashion. The ground rod is doing nothing. As soon as a well-grounded animal makes adequate wire contact, energy passes through the animal...into the ground...and over to the ground rod. It's that simple. What's not simple is assuring good grounding of the rod and the animal, or adequate wire contact. The less powerful your charger, the more important these things become.
The problem with most electric fences (no matter their intended target) is getting adequate energy to move from the hot wire...thru the animal...and into the ground. You can run a 2-wire setup with hot and ground wires in proximity circling the fence, but this requires the animal to contact both wires simultaneously. That's the equivalent of touching the hot and ground wires simultaneously. It's more effective but more work and a bit more weight. You still need a good ground rod into moist earth, but a 2-wire rig is less dependent on the animal itself making ground contact.
Most of us are using a conventional all-hot fence with the charger grounded to earth. This works great as long as the animal is also making good ground contact along with adequate wire contact. If the animal is standing on dry vegetation it will serve as an insulator from current passage. If only their thick hair makes contact they may never feel a thing unless they are well grounded. You'd ideally like the animal standing on bare ground (soil contact) and touching the wire with their nose or other short-hair part. A good electric fence has enough power to actually arc energy across space and to the skin. I've witnessed this myself as a visible spark jumps from the wire to a dog's or cow's nose or skin. Pain!
The lesson here is get a solid ground rod or spike established. Check it with a good test unit. Use enough energy to help overcome some expected resistance. Clear the ground outside the fence. I've taken strips of aluminum foil (think size of a hot dog) and wrapped them around the fence wire at spaced intervals. The idea is to catch a bruin's attention and have them nose or lick the foil when they approach the fence. Zing!