In the play, Menenius Agrippa is a foil for Coriolanus. While Coriolanus is blunt and sometimes callous in his speech, Menenius is ever the smooth-talking, silver-tongued politician.
As an illustration, both men relate to the public in uniquely different ways. In Act 1, Scene 1, Menenius addresses the populace with consummate courtesy and grace. He addresses them as "good friends" and "honest neighbors." When he discovers that the citizens intend to revolt against their leaders, Menenius takes steps to calm the mob down. First, he assures them that the patricians' chief aim in life is to care for the people who rely on them. Then, he tells them a little story that appeals to their emotions (Menenius is, after all, a politician, and he is certainly well-versed in the art of rhetoric).
Basically, Menenius equates the patricians to the stomach in a body; its chief purpose, as the "store-house and the shop of the whole body," is to apportion the body's resources to the rest of the body. Contrast Menenius' skillful gallantry with Coriolanus' brash sullenness as the latter appears before the mob:
What's the matter, you dissentious rogues,
That, rubbing the poor itch of your opinion,
Make yourselves scabs?
What would you have, you curs,
That like nor peace nor war? the one affrights you,
The other makes you proud. He that trusts to you,
Where he should find you lions, finds you hares;
Where foxes, geese...
I'll make a quarry
With thousands of these quarter'd slaves, as high
As I could pick my lance.
And let me use my sword, I'll make a quarry
With thousands of these quarter'd slaves, as high
As I could pick my lance.
Coriolanus loses no time in insulting the populace; he calls them "curs" and insinuates that they are untrustworthy as well as fickle. If he had his way, he would have them all quartered and heaped into a mountain as high as he could pitch his sword. Meanwhile, Menenius tries to persuade Coriolanus to calm down, explaining that "these are almost thoroughly persuaded."
In other words, Menenius is quite willing to manipulate the people to further his own ends. He isn't any more inclined towards the common citizenry; he's just better at hiding his true emotions. Later, in Act 3, Scene 3, it is Menenius who covers for Coriolanus again when the latter insults the plebeians and their tribunes.
It should be noted that Menenius is an extremely ambitious character; he knows that his position as Coriolanus' informal chief public relations officer will benefit him in the long run. After all, to be an aide to a future consul is no small feat. So, Menenius convinces Coriolanus to swallow his pride and to submit himself to the will of the people. Coriolanus reluctantly agrees, and Menenius smooths the way by reminding the plebeians that Coriolanus is a soldier and that he's used to speaking bluntly.
Menenius advises the people not to interpret Coriolanus' "rougher accents for malicious sounds." In Act 2, Scene 1, Menenius draws attention to Coriolanus' war injuries, and in Act 3, Scene 1, he reminds the people that Coriolanus "has been bred i' the wars/ Since he could draw a sword, and is ill school'd/ In bolted language." Menenius tries to portray Coriolanus as a war hero who is worthy to be consul. In short, Menenius sees himself as Coriolanus' mentor; in his mind, Coriolanus needs a steady adviser to help him navigate his way through the political jungle. However, as can be seen in Act 5 (when Menenius tries to warn Coriolanus against invading Rome), Menenius' judgment regarding his protege sometimes proves faulty. He isn't as influential as he thinks he is, especially when Coriolanus is set on a particular path.
In all, the relationship between both men is complex, ambivalent, and sometimes contentious.