Runners often substitute cycling to maintain leg strength and sometimes to help improve running speed. Cycling is a good substitute when you are not able to run as it does involve the same muscles but not to the same degree.
For example, cycling relies mainly on the quadriceps in leg extension. It is a dynamic move that powers the cyclists forward.
For runners, the quadriceps are used mainly for preventing excessive lowering of the body after touchdown. In addition it is used to create the vertical forces when pushing off in runners with poor technique who push off when the body is above the support foot.
Thus the emphasis in both sports is different. Runners require more of a holding contraction while cyclists need an active powerful leg extension movement.
However, this does not mean that you should not substitute one for the other. Depending upon your level of fitness, cycling can be a good substitute for runners mainly for aerobic development.
In regard to the calves, that are responsible for ankle extension, the key action for forward propulsion in running, strengthening this muscle is much more important for runners than it is for cyclists. To get greater emphasis of this muscle when cycling it is important that the runner concentrate on ankle extension at the tail end of the down stroke.
The hamstrings play an important role in running — if you have good technique and execute the pawback movement. If not, and if you are a heel hitter, the hamstrings play a completely different role. In this case they act more as absorbers and preventers rather then creating forward propulsion.
To learn more about the muscles involved in running and how they relate to running technique read Explosive Running and/or Build a Better Athlete.