It's just like regular Krabby Patty, but are sponsored by the Krusty Plankton.
Role in episode
Plankton offers a Planky Patty to his grandmother, but she accidentally drops her dentures on the grill. She has Squidward chew it up for her and feed its chewed-up state to her. Afterwards, she deems the Planky Patties to taste delicious.