Why do Cassius, Cinna, and Casca want Brutus to join their cause? What does this reveal about what they think of their cause? It's in Act 1, scene 3.
Cinna, Cassius and Casca need the legitimacy that Brutus can bring to their conspiracy. They want to assassinate Caesar, but they want this act "spun" so that it doesn't look like a treasonous power play. They, and in particular, Cinna, know that, like Caesar, Brutus is popular: he "sits high" in the hearts of the masses. His "countenance," literally his face, but meaning here his presence, his stature, his reputation, will change what would look like a crime if the other three acted alone into a noble deed.
This reveals that the three know they are stepping into illicit territory. They know what they are doing has to come across to the citizens of Rome as the right step. They know they are a taking a risk and want to minimize the potential damage as far as they can. They realize they have to "cover" this murder with the appearance of virtue. They realize they need a powerful ally like Brutus.
The other conspirators (Cassius, Cinna, and Casca) want Brutus to join their cause because they feel he would add credability to their cause. People care about Brutus and respect him, as he has a good reputation. However, Cassius, Cinna, and Casca are not as well known. In fact, some would question their motives, as most of Rome is currently on the side of Caesar, as evidenced by the large crowds hailing him and begging him to be their king.
This shows that the conspirators do not have confidence in their cause, or that they feel they do not have support of the masses. In order to have a successful government takeover, they must have the people's support. By enlisting the help of Brutus, they feel they will gain more respect and credability in the eyes of the people.