Watney was on the Ares III mission. Missions up to Ares V were in the works, and equipment such as the MAV (Mars Ascent Vehicle) were already in place on Mars, waiting for these missions to arrive. The amount of equipment necessary for each mission was split into separate launches to reduce the individual payloads.
Shortly after Watney discovers he's stranded he mentions the Ares IV MAV is already on-planet, though it is far away - much further away than the buggy can take him. Needing to reach the Ares IV mission site (where the Ares IV MAV is already) is what prompts him to start retrofitting the buggy for longer journeys.
The MAV is an ascent vehicle, only designed to get its occupants into Mars orbit, and not much else. The Hermes should have been in Martian orbit when the Ares IV MAV launched, and the MAV would have no trouble reaching the ship.
However to rescue Watney the Hermes' return trajectory involved a slingshot around Mars, intentionally avoiding entering orbit so they'd be able to return home. This meant the Hermes was going significantly faster than the speed the MAV was designed to intercept at. In order for the MAV to gain enough velocity, its weight had to be reduced.
This is all explained in-movie (though some of it's easy to miss), see it again and you'll catch all these details.
A previous answer had several inaccuracies that are also worth clarifying:
- The MAV was not "designed to reach Mars", its sole purpose (hence the name) is to get the crew off Mars. It was delivered to Mars as part of a larger payload.
- The crew does not leave in the same ship they arrive in; they leave in the MAV, which is already on-planet.
- The Chinese rocket is not used as a booster to propel the Hermes. It contains necessary supplies to sustain Watney (and the crew of the Hermes). The Hermes is able to return to Mars via a gravity slingshot.