Rest only means rest from running, not complete bed rest! Other activities are fine - it's called cross-training. It's a good idea to have a day of complete rest once a week, though

Cycling makes excellent cross-training for runners, because it works your quads, which running doesn't do much for. If you only run, you can develop a muscle imbalance with weak quads and strong hamstrings, and since your quads stabilise your knees, the result can be knee problems. So cycling helps protect the runner from injury.