Marullus and Flavius, the two Tribunes who appear only in the play's opening scene, are alarmed at Caesar's triumphant return after defeating his rival and former co-ruler Pompey. This victory, celebrated with a great procession, leaves Caesar as the single most powerful man in Rome, and Marullus and Flavius are concerned that he might go on to impose one-man rule. As Rome is a republic, many political observers, like Marullus and Flavius, feel that this cannot be allowed to happen. They therefore determine to try and put a stop to him, and to symbolically 'disrobe' (I.i.65) the images of him that have been erected in the streets.
These growing feathers pluck'd from Caesar's wing
Will make him fly an ordinary pitch,
Who else would soar above the view of men
And keep us all in servile fearfulness. (I.i.73-76)
Flavius here uses an image of Caesar as a bird who is flying too high and therefore must be brought back down to the 'ordinary' level of men. This idea is developed throughout the play; the misgivings expressed by the Tribunes will be taken up by Cassius and Brutus, eventually leading to Caesar's assassination.
Flavius and Marullus are not just upset at Caesar, but also the way that the citizens of Rome celebrate his return. The Tribunes rebuke the people sharply for extolling Caesar when, previously, they had turned out to support Pompey. This fickleness of the crowd is a major theme of the play as a whole. The people do not care for political niceties; it seems that they just cheer on anyone who happens to be winning and is able to put on a fine show or make a rousing speech (as also seen, crucially, at Caesar's funeral). The Roman republic means little or nothing to them, and this draws the extreme ire of the two Tribunes.
Marullus and flavius are upset that Caesar will return because they know what Caesar will become dictator, and being the tribunes, puts them in danger. They were right, for Caesar has them killed.