The flight had two primary objectives. The first was to deploy the Long Duration Exposure Facility (LDEF), a passive, retrievable, 12-sided experimental cylinder. The 21,300-pound (9,700 kg) LDEF was 14 feet (4.3 m) in diameter and 30 feet (9.1 m) long, and carried 57 scientific experiments. The second objective of STS-41-C was to capture, repair and redeploy the malfunctioning Solar Maximum Mission satellite ("Solar Max"), which had been launched in 1980.

On the second day of the flight, the LDEF was grappled by the "Canadarm" Remote Manipulator System (RMS) arm and successfully released into orbit. Its 57 experiments, mounted in 86 removable trays, were contributed by 200 researchers from eight countries. Retrieval of the passive LDEF was initially scheduled for 1985, but schedule delays and the Challenger disaster of 1986 postponed the retrieval until January 12, 1990, when Columbia retrieved the LDEF during STS-32.

On the third day of the mission, Challenger's orbit was raised to about 300 nautical miles (560 km), and it maneuvered to within 200 feet (61 m) of the stricken Solar Max satellite. Astronauts Nelson and van Hoften, wearing spacesuits, entered the payload bay. Nelson, using the Manned Maneuvering Unit (MMU), flew out to the satellite and attempted to grasp it with a special capture tool, called the Trunnion Pin Acquisition Device (TPAD). Three attempts to clamp the TPAD onto the satellite failed. Solar Max began tumbling on multiple axes when Nelson attempted to grab one of the satellite's solar arrays by hand, and the effort was called off. Crippen had to perform multiple maneuvers of the orbiter to keep up with Nelson and Solar Max, and nearly ran out of RCS fuel.

During the night of the third day, the Solar Max Payload Operations Control Center (POCC), located at Goddard Space Flight Center, Greenbelt, Maryland, was able to establish control over the satellite by sending commands ordering the satellite's magnetorquers to stabilize its tumbling. This was successful, and Solar Max went into a slow, regular spin. The next day, Crippen maneuvered Challenger back to Solar Max, and Hart was able to grapple the satellite with the RMS. They placed Solar Max on a special cradle in the payload bay using the RMS. Nelson and van Hoften then began the repair operation, replacing the satellite's attitude control mechanism and the main electronics system of the coronagraph instrument. The ultimately successful repair effort took two separate spacewalks. Solar Max was deployed back into orbit the next day. After a 30-day checkout by the Goddard POCC, the satellite resumed full operation.

Other STS-41-C mission activities included a student experiment located in a middeck locker which found that honeybees can successfully make honeycomb cells in a microgravity environment. Highlights of the mission, including the LDEF deployment and the Solar Max repair, were filmed using an IMAX movie camera, and the results appeared in the 1985 IMAX movie The Dream is Alive.