What are the two mobile pressure vessels?

The mobile pressure vessels are the rover and the trailer.
The two vessels aren't completely independent; they're connected by a hose. The rover is more important because, as Mark Watney says, "If the rover breaches, I'm dead." He can live without the trailer, so he decides that he's going to pack all the essentials in the rover. That way, if the trailer dies and he has to continue on with only the rover, he still has what he needs to stay alive.
If the hose connecting the two vessels breaks, the other vessel seals the line that keeps things pressurized. This is why the trailer can die and he'll still be fine in the rover. According to Watney, the rover can have the regulator going for a month on one battery charge as long as he doesn't drive it and doesn't use the heaters.
The team on the ground doesn't know how long he's planning to take to get the modifications to the rover done. Venkat says that Watney only has 16 sols to complete them.