Walking does build muscle but only to a limited extent.
Walking mainly engages your lower body muscles which include your quadriceps, glutes, hamstrings and calves.
And as you walk, these muscles which include the calves, glutes, hamstrings and quadriceps repeatedly contract and lengthen, which helps to strengthen and tone them.
Walking alone though is not enough to build significant muscle mass.
If you want to maximize your muscle growth and build significant muscle you should combine the walking with resistance training or weight lifting.
Walking is a low impact form of movement and exercise so it won't give you the large muscles that you would get from lifting heavy weights.
However by upping the intensity, pace, frequency and resistance of the walking you can help to stimulate the muscle growth and increase your lean muscle mass.
And while walking mainly improves your cardiovascular health as well as endurance, walking can help with muscle toning, especially in the legs and glutes as a result of the resistance against gravity and repetitive motion.
Walking mainly activates the slow t-witch muscle fibers that are responsible for building muscular endurance and resistance to fatigue.