The Dimmadome is a complex owned by Doug Dimmadome, and the official home court of the Dimmsdale Ballhogs (who nearly got sent to Alaska due to being in last place, but thanks to Timmy they learned to share and were able to save themselves from going there).
Nearly every major sporting event that takes place in the city of Dimmsdale is hosted here at the Dimmadome, and the structure itself is a landmark of Dimmsdale. Usually when a wish changes the city, the Dimmadome will return in some form changed by the wish. For instance, in "Future Lost" the Dimmadome was flying in the sky along with the rest of the city.
Although the exact details of the Dimmadome change between episodes, in most depictions it is a Coliseum-style circular structure with the words "Dimmadome" written along the side, and Roman-style archway entrances into the stadium.