Brutus is a tragic hero because he's basically a good man brought to grief by a fatal flaw. Brutus is a noble man who wants to do what's best for Rome. He believes in the Roman Republic and genuinely believes that Caesar is a threat to its values. As far as he's concerned, Caesar wants to make himself king and turn Roman citizens into little more than slaves.
However, Brutus's nobility is also his fatal flaw. He's so concerned with doing what's right and noble that he overlooks important matters. For one thing, he doesn't stop to question the somewhat less-than-noble motives of his fellow conspirators, such as Cassius's. Furthermore, he's so fixated on the bigger picture, on his exalted role in a gigantic cosmic drama in which he's the hero, that he overlooks crucial details concerning military planning and preparation, leading to defeat and to his own tragic death.