The purpose-built facility repaired friendly ground vehicles at a cost (proportional to the vehicle's damage) and remove terror drones. A service depot was also required to construct an MCV.
In a similar fashion, naval units could be repaired at the naval shipyard, although the amphibious transport could be repaired at the service depot as well. In both cases, repairs would stop if the commander runs out of resources.
The service depot was considerably more important to the Soviets than the Allies. In the absence of a Tech Outpost or Tech Machine Shop, it was the only way Soviet battlefield commanders could repair vehicles (unless the vehicles were self-repairing, such as elite units and Apocalypse tanks), while the Allies could use an IFV with an engineer inside it to repair their ground units and remove terror drones at no extra cost to the commander.
In Red Alert 2, there was a glitch where any vehicle (except for the Amphibious Transport) that stopped on the Service Depot but wasn't given the order to enter the depot for repairs was instantly destroyed. This was not present in Yuri's Revenge.