Answer
The red light does not have enough energy to develop the black-and-white film, but provides enough light to allow someone to see what they're doing in the darkroom. Color film would be too sensitive for this.
Work Step by Step
See Figure 27-4. The red bulb’s filament is cooler than a regular old-fashioned “white-bulb” filament, and thus emits much less radiation in the middle of the visible range that the black-and-white film is especially sensitive to. The red light still allows a worker to navigate his/her way around the room.
Such a bulb would not work well around color film; The photos would have a red tint to them.