There are several reasons why Brutus is very important. Let me give you a few of the these reasons.
First, from a historical perspective, Brutus was incredibly important as one who stood for the Republic. Hence, for Shakespeare to have some historical semblance he had to use Brutus. Moreover, Brutus' great ancestor of the same name established the Republic. Hence, republican ideas ran in Brutus's family.
Second, from a more literary point of view, Brutus is the tragic hero of the work. On the one hand, he loved Caesar and respected him as a friend. The affections were genuine. There is no doubt on this point. On the other hand, he loved the Republic and when he went against Caesar, he did so as a man of virtue and principle. He really believed that Caesar was putting an end to the Republic. From this perspective, Brutus was the only honorable conspirator. The rest of them acted out of jealousy and envy; Brutus acted in honor.