Pocket is the Villager's standard special. It picks up any projectile or item and saves it for later use.
There are many uses for this attack, stuff like Zelda's Phantom, Samus's Charge Shot or Sonic's Spring can all be grabbed and used in differnet ways. The attacks give Villager the quick knockback he normally lacks.
It's also a good strategy to pocket recovery items since they can used later when percentage is high.
It cannot be used on Assist Trophies though.
The move originates from the Animal Crossing games where the pocket is where various items including bugs, furniture, fish, fruit and sometimes stuff like snowflakes. The all-consuming nature of it is similar across both series in that it can pick up objects regardless of their size.