The song is centered around average people (or people in general) dying in modern times.
Most of the main characters are his friends from high school, as revealed by one of the characters' sons.

From Texas Monthly:

“Pepper,” which originated as a recorded drumbeat and a guitar riff by Paul Leary, drew on the memories of singer Gibby Haynes, who scribbled out lyrics about people he had known as a teenager in Dallas (Mikey, Sharon, another Mikey, and “the ever-present football player rapist”) who’d lost limbs and lives to fights, car crashes, and AIDS. The one thing they’d had in common: “They were all in love with dying, they were doing it in Texas.”