The solenoid controls the pneumatics. Specifically, it allows air to go to a cylinder (or other pneumatic device). It is wired to a relay or the solenoid breakout.
Pneumatics are not necessarily wheel types here. Some teams have used inflatable wheels in the past, but not this year. Take the compressor and the two round silver accumulators out of the KOP. Those are pneumatics. They compress and store air for use on the robot; cylinders turn that air pressure into linear motion. Think hydraulics, but with air.