They look extremely similar in appearance to SpongeBob's regular pants, but are round in shape.
Role in episode/books
SpongeBob leaves his pants in the dryer for too long, due to Patrick making him wait too long on the phone with his spluttering, which causes them to shrink, leaving him no other choice but to go buy a new pair of pants. While at the store, he tries to find a pair of pants that he likes, but all of the ones he tries on are either too long, too wide, or just plain weird. However, he finally finds a pair that suits his needs, which are no other than a round variant of his usual pants.
While walking down the street, none of SpongeBob's friends recognize him anymore due to the fact that he's no longer wearing his signature clothes. As he almost gets home, SpongeBob goes up to Squidward and says "hi" to him to see if he'll recognize him. Squidward pretends to be unaware of SpongeBob's identity so he won't have to talk to him. AAfterward SpongeBob becomes sad that no one recognizes him anymore all because of an outfit change, so he resorts to starting all over again. He then notices the Krusty Krab and is immediately cheered up.
Once SpongeBob RoundPants enters the restaurant, he walks up to Squidward's workstation and applies for a position. Squidward realizes that his plans to pretend not to be aware of SpongeBob's new identity failed, leaving Squidward no choice but to play along. Squidward then introduces Mr. RoundPants to the restaurant and shows him how he does his job. RoundPants picks up all of Squidward's bad habits and starts getting the hang of the job.
Mr. Krabs then storms out of his office and is disappointed to see an angry line of customers. He is used to Squidward sleeping on the job but expects better from Mr. RoundPants. SpongeBob tells Mr. Krabs that he cannot be SpongeBob SquarePants again, as he has round pants. Mr. Krabs asks him who told him this and SpongeBob states it was Patrick, who stops eating a Krabby Patty when he realized his error of not recognizing SpongeBob in the first place. As a result, RoundPants is forced to remove the pants.
SpongeBob is then happy that he's back to his normal self. However, once Sandy walks into the Krusty Krab and realizes what SpongeBob is wearing, he calls him "SpongeBob UnderPants," leading SpongeBob to scream and realizing that he has to start all over yet again.