Where did Mark Watney get the escape pod in The Martian?

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.

Ankit is close. And maybe I'm not quite reading it correctly, but here is what I understand:

• As Ankit stated, this rocket was 'shipped' to mars ahead of time for a future mission.
• This rocket didn't deliver materials. Rather, it's the rocket that takes the crew off of mars into Mars' orbit when they finish their mission. This is the same type of rocket the crew escaped from Mars with in the first part of the film.
• The reason it didn't have enough energy to reach the crew was that the crew couldn't get their ship into Mars' orbit. So they had to lighten the launcher as much as they could so they could get it as high as possible to intersect with the crew that was sling-shotting around Mars.

The MAV could never have rendezvoused with Hermes at a 5 m/s relative velocity. Hermes was in a hyperbolic orbit around Mars, meaning it was at escape velocity the entire time -- why it was called a flyby. Watney's MAV could only put him into low Mars orbit, made slightly higher by stripping down the MAV. The physics problem is that at any orbital height, escape velocity is always 1.4 times orbital velocity.

If Hermes flew past Mars at 600 km altitude it would be traveling at least 1.4 times as fast as the MAV at that height, since the MAV could not achieve escape velocity. In orbit, speed translates into orbital height. Remember, he had no power after the initial thrust; he was totally in a ballistic orbit. At any altitude in in Hermes' hyperbolic orbit he could reach, he would be traveling much slower than Hermes, and any speed of Hermes he could match, he would be much lower.