Apollo 13 was the seventh mission of NASA's Project Apollo. It was the third lunar-lander mission with a crew. Jim Lovell commanded Apollo 13. The other astronauts were Jack Swigert and Fred Haise.
The craft launched successfully toward the Moon, but two days after launch a faulty oxygen tank exploded. It damaged the Service Module. It lost oxygen and electrical power. There was a very large chance that the astronauts would die before they could return to Earth. They were very short on oxygen. Oxygen is not just used to breathe; on the Apollo spacecraft it was used in a device called a Fuel cell to generate electricity. So they saved their remaining air by turning off almost all their electrical equipment, for example heaters. It became very cold in the spacecraft.
The astronauts also had to move into the Apollo Lunar Module to survive and use it as lifeboat.
When they approached the Earth they were not sure that their parachutes, needed to slow the Command Module down, would work. The parachutes were thrown out by small explosive charges that were fired by batteries. The cold could have made the batteries fail, so the parachutes would not work and the Command Module would hit the ocean so fast that all aboard would be killed.