The Senate is a council of ten senators elected from the legion at Camp Jupiter. It gathers in the Senate House of New Rome where the senators discuss issues that arise, such as deciding whether or not quests are to be granted or whether or not to go to war. All known senators are either a centurion, a praetor, the augur, the Pontifex Maximus, or a god's ambassador.
The senate met to see whether or not to give a quest to Alaska since it went against regulation to lead the gods realm of power, but since it was given to them by Mars, the quest was granted. After the battle with Polybotes, the senate convenes to decide whether or not they should allow the Argo II to land.
Jason says the senate is going to elect him Pontifex Maximus.