The Mud Gate is a location in the second season. It is a gate in the walls of King's Landing that opens near the shore of Blackwater Bay.
Tyrion Lannister predicts that it will be the focal point of King Stannis Baratheon's attack because it is weak and easy to land near.
In the books
The official name of this gate is actually the "River Gate", but it's commonly known as the "Mud Gate".