They are napkins with SpongeBob's face imprinted on them. According to Mr. Krabs, they are extra absorbent to reflect the species of a sponge.
Role in episode
After SpongeBob becomes immensely popular as a result of food critic Gene Scallop's review of the Krusty Krab, Mr. Krabs decides to rename his restaurant to the "Krusty Sponge." Many SpongeBob-themed items are produced for the restaurant, including these napkins.
Squidward thinks that Mr. Krabs should go see a doctor for this creation amongst the many other SpongeBob products.
SpongeBob napkins have been marketed in real life before.