People could not walk without friction. what friction are we talking about here, kinetic friction or static friction?

When there is relative motion between surface and the contact, the friction acting is kinetic friction. But when there is no relative motion between surface and the contact then the friction is said to be static friction.

When we walk, we try to push the ground behind in order to move forward. But the relative motion between your leg (contact with the surface) and surface is zero, therefore it is static friction.