What is the walking force that provides movement for a person? How is it directed?

The movement of a person when walking is provided by the friction force.
When a person takes a step, he kicks off the ground. In this case, the sole of his shoes tends in the opposite direction to the direction of the person’s movement. And the friction force acting from the ground on the sole is directed against the movement of the sole.
If there is enough friction to keep the foot from slipping on the shoe, then the foot will not move during the push. In this case, the friction force will be equal to the static friction force. If the foot slips, then the sole moves back, the head stays in place, and the person falls.