When Brutus gave his speech of why he was part of the conspiracy and his rationale for the slaying of Caesar, the people were moved. Brutus' speech about how he loved Rome more than Caesar made a lot of sense to them, especially when he tied it to the idea of the freedom of the Roman citizen. We must bear in mind that the exile of the kings in early Rome was something that the Romans were proud of. More importantly, it was Brutus' ancestor, another Brutus, that drove out the last king.
So, the crowd cheered Brutus on. Some even suggested that the people should erect a statue of him. One person even said that he should be Caesar! From this perspective, Brutus' speech was very successful.