David Gahan sings throughout the Spirit album about his and his bandmates' disenchantment with the state of the world. He expresses their opinion on this song by telling a story. "It's about a person who travels to another planet only to find that, much to his dismay, it's exactly the same as earth," Gahan told Rolling Stone. "It's a different planet but the same. He really can't get away from himself. If he wants things to change, he's going to have to implement it."
The black-and-white music video was directed by the longtime Depeche Mode collaborator, Dutch photographer and filmmaker Anton Corbijn. "A big surprise for me was how 'Cover Me' ended up being," Gahan told NPR regarding the clip. "I always heard this idea of the song being in two halves. The song is here and then you kind of get in the spaceship and go somewhere else."