Menenius is Coriolanus' friend, father figure, campaign manager, and spin doctor—which obviously means that he's a patrician. (Coriolanus definitely doesn't hang with any of the commoners, after all.)
Menenius has the resume to manage Coriolanus' campaign: he's one of the smoothest-talking politicians in Western literature. Case in point: he stops a riot in its tracks by telling the angry plebeians a little fable to calm them down. Just as the plebs are ready to tear Coriolanus apart with their crude weapons, Menenius steps in and has them eating out of the palm of his hands in no time at all (1.1.124-163). (Check out "Symbols: The Fable of the Belly" for more details.)
Of course, Menenius never actually addresses the peoples' biggest gripe, which is that they are literally starving. (No biggie.) Instead, he wins them over by pandering to and manipulating the "rabble," who are too dumb to notice they're being manipulates. In fact, the plebeians think Menenius is the greatest guy ever. They believe he is "honest" and call him "Worthy Menenius Agrippa, one that hath / always lov'd the people" (1.1.51-53).
Sounds to us like Menenius is more of an actor than a warrior. No wonder he's such a good politician.
Of course, Menenius doesn't love the plebeians any more than Coriolanus and the other patricians do. In fact, he thinks they're all a bunch of idiots and never, ever takes their side when they complain about the social and political inequality in Rome. But he's so good at pretending to love the common people, that he's the most successful politician in the play.
In this way, he functions as a foil to Coriolanus, who's the play's least successful politician. Coriolanus always speaks his mind, even when it's totally going to get him in trouble. And what does that get him? The label of "chief enemy to the people" (1.1.7-8).
When Coriolanus runs for consul and says all the wrong things to the voters, Menenius has do some careful PR work. Check out how he tries to do damage control after Coriolanus insults the Citizens with his abusive language:
That when he speaks not like a citizen,
You find him like a soldier: do not take
His rougher accents for malicious sounds,
But, as I say, such as become a soldier,
Rather than envy you. (3.3.52-57)
Basically, Menenius is trying to turn Coriolanus' rough mannerisms into a positive character trait. By blaming Coriolanus' harsh and abusive language on the fact that he's a soldier, Menenius is also reminding the voters that Coriolanus is a war hero who has saved Rome from its enemies on numerous occasions. Pretty crafty.