Walking is the application of:

According to Newton's third law, when two bodies contact, they apply forces to each other that are equal in magnitude and opposing in direction. The third law is also known as the action-reaction law.

According to Newton's third law, every action has an equal and opposite response. This is crucial to walking because you impart force to the earth when you put your foot down. 

In doing so, the earth applies an equivalent force to your foot in the opposite direction, propelling you forward.