The statue is a large, gray replica of Squilliam Fancyson holding a trash bag and a trash picker. On the bottom is a golden-colored plaque that reads "Squilliam Fancyson," along with other illegible writing. This was rewarded to Squilliam after he cleaned Bikini Bottom in one week, therefore the reason why the the trash bag and trash picker are on the statue.
Role in episode
When Squidward lies to Squilliam about him picking up trash as community service and that he is voluntarily doing it, the latter mocks him, saying that they might make a statue for Squidward cleaning Bikini Bottom, only to point out they made one of himself. Squidward then says that he'll get one for cleaning Bikini Bottom in one day to spite Squilliam.
Later, Squidward's statue, made out of garbage, melts Squilliam's statue by its smell. Officer John Slugfish then gives Squilliam a ticket due to "littering" with the melted statue.
Squilliam's statue doesn't feature Squilliam's unibrow. One possible reason is that he doesn't want his monobrow to be featured on the statue or it is just an animation error.