They say running is a complete exercise because it is the only form of exercise where you use nearly every muscle in your body. Although that is truth there are major muscles used while running.
The major muscles used while running are calves, hamstrings, quads and many other muscle in your leg and lower body.
Calves – they help in pushing you off the ground.
Quads – they help stabilize the leg upon contact with the ground
Hamstrings – they help to propel you forwards.
For a good and through explanation of how this muscles work visit wikipedia running page.