Walking Pokémon are Pokemon that walk alongside their Trainer when they're normally would be inside the Poke Ball.
IN the anime
Pikachu riding on Ash's shoulder.
The most obvious example is Ash's Pikachu. During Ash's first day as a Pokemon Trainer, Pikachu adamantly refuse to be inside the Poke Ball after being sent out by Professor Oak, and afterward revealed to Ash that he didn't like being inside the ball, thus Pikachu often ride on Ash's shoulder or head.
Another example is Iris' Axew, as instead of staying inside the Poke Ball, he enjoys staying on Iris's hair.
