They look extremely similar to SpongeBob's regular pants, but are round in shape.
Role in episode/books
SpongeBob leaves his pants in the dryer for too long, 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 is 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 will recognize him. Squidward pretends to be unaware of SpongeBob's identity so he does not have to talk to him. Afterward 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 enters the restaurant, he walks up to Squidward's workstation and re-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 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 when he realizes his error of not recognizing SpongeBob in the first place.
As a result, SpongeBob is forced to remove the pants, gladly returning to his previous identity.