The Senate was a government building which housed the government of Prisma City.
Prior to the general election, as Blob flew over the Senate building (fired from the Canon back in Paradise Island), he saw the the parties inside in complete chaos. (Note that the Senate was bleached at this time).
During the general election, Papa Blanc (Comrade Black in disguise) rigs the results of the election by rigging each voting booth. The booths had a artificial arm which would either force the visitors to vote for Blanc, or would do it themselves. Unsurprisingly, when the results came out, it showed that Papa Blanc had won by a clear majority. After the results, Blanc gave a villainous laugh before revealing his true identity before a reporter; and hence, everyone, before a group of Inky Soldiers stood behind him and the reporter fled in fear.
Blob later reached the Senate to liberate it from INKT. After fighting through the building and destroying a turret wheel, Comrade Black fled from the building, along with his two bodyguards, just before it was transformed to its true self.
Not much is said about the Senate until Rocket Range, where PNN (Prisma News Network) states that the Senate has reopened and the senators passed a pro - color bill before heading out to lunch. After Blob defeats Black and the Hypno-Ray is destroyed, Blob crashed in front of the Senate wearing Prof's Engine Pants before meeting with his friends.