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.
There are several reasons why Brutus is considered the tragic hero of Julius Caesar. The most direct reason is because he is the only one that has noble motives throughout the entire play. In the last scene, Antony calls him the most noble Roman of them all, and the only one of the conspirators that did not kill Caesar out of ambition or jealousy. Another reason that he is the tragic hero is because of the reputation that he holds in Rome. He is well liked and well respected, which is why Cassius writes forged letters from Roman citizens claiming that assassinating Caesar is the only way to save Rome. Finally, he is the tragic hero because he very blindly trusts others, which eventually leads to his death. This is seen not only in his relationship with Cassius, but also in his dealings with Antony. He gives Antony total freedom to say and do whatever he wants at Caesar's funeral, believing that he truly understands the motives of the conspirators. This begins the war that ends in Brutus's death.