The drive phase is a combination of how powerfully you contract and engage your hip extensors, glutes and hamstrings to pull the leg under and behind you as you touch the ground. The more powerful your hip extension, the faster you will go. The drive phase of hip extension is brief and shouldn't be confused with forcing the leg backwards.
Once you've initiated hip drive and generated power through the hip, you should relax and let the leg travel behind you naturally. The distance or degree to which your leg travels behind you will correlate directly to how much force you generate during the drive phase. Therefore, there is no reason to force the leg backwards; it will happen naturally.
More: Hip Strengthening and Mobility Exercises for Runners
Recovery Phase
After you've driven your leg back, the stretch reflex of the hip flexors kicks in and begins to propel your leg forward. A common misconception about the role of the hamstrings during this phase of the running gait is that they should contract to bring the heel closer to the butt (which occurs to shorten the lever as the leg swings forward).
However, bringing the heel towards the butt actually requires very little activation of the hamstrings; electrographic research suggests it's as little as 7 percent.
The movement of the heel towards the butt is aided by the stretch reflex generated during hip extension. This is why the faster you run, the closer your heel will get to your butt without conscious effort on your part. But, if you consciously try to bring the heel towards the butt by contracting the hamstrings, you'll waste energy.
More: Should You Change Your Running Form?
How to Strengthen Your Hip Extensors, Glutes and Hamstrings
Now that you understand how the biomechanics of hip drive work, you can better target your stretching, drills and strength work to improve exactly how these muscles function during the running stride. Here are some stretches, drills and exercises to get you started:
Theraband Drive Back
With your foot or heel attached to a cable machine, stand facing the structure that the cable is attached to. Balance on one foot (it's OK to hold on to another object for balance) and bring your leg slightly in front of you. Drive backwards with your foot in the band. Focus on generating the movement from your glutes and hamstrings. Slowly bring the leg back up and repeat. Complete one set of 20 to 25 reps on each leg.