Sicinius and Brutus are two scheming tribunes elected by the plebeians. After the plebs agree to vote Coriolanus as Rome's new consul, the tribunes convince the people to take back their votes (2.3). They're also the ones who proclaim Coriolanus' banishment from Rome (3.3).
The tribunes are supposed to represent the peoples' best interests and keep their rights from getting trampled all over. But Sicinius and Brutus seem more interested in exploiting the tense social and political conflict between the plebeians and the patricians in order to gain personal power. They can't stand Coriolanus, so they spend all their time plotting his destruction and downfall. In fact, they basically run a smear campaign against Coriolanus and accuse him of acting like a "tyrant." (How's that for an attack ad?)
We could argue all day long about whether or not Coriolanus is a wanna-be tyrant. What's inarguable is that the tribunes act a like Coriolanus is a bigger threat than they actually think he is. When they succeed in getting Coriolanus exiled from Rome, Brutus says "Now we have shown our power, / Let us seem humbler after it is done / Than when it was a-doing" (4.2.4-6).