Walking is a form of ground-based movement slower than dashing. It is performed by pressing forward on the control stick or d-pad while on the ground. While it is slower than dashing (though by exactly how much is dependent on the character), characters retain the use of their tilts and smashes while walking, giving it some technical use. Characters have three different walking speeds depending on how far the control stick is tilted, with the slowest of these animations often being a sort of tip-toeing. However, when if being controlled with a Wii Remote, characters always walk at their max speed. As implied earlier, hitting the attack button while walking will result in a forward tilt. Because of this, it can be considered an advantage to have a fast walking speed. This is especially true for characters like Squirtle, Marth and Donkey Kong.
Super Smash Bros. walking speeds
Super Smash Bros. Melee walking speeds
Super Smash Bros. Brawl walking speeds
Super Smash Bros. 4 walking speeds
Super Smash Bros. Ultimate walking speeds
Super Smash Bros. for Wii U digital manual description