What does mining rig mean?
A machine/computer specifically designed to solve the PoW puzzle in the most power efficient way. Mining rigs these days are equipped with a specialized ASIC chip that has been designed specifically for the task of mining Bitcoin.
Other coins that support ASIC mining also have chips specifically designed for that coin type. Some coins are considered ASIC resistant and can still be mined using the computer’s CPU or GPU. In these cases the mining rig may be no more than a person’s home computer or laptop. When large groups of mining rigs are combined in a central location this is known as a mining farm.