This is a fantastic question. I think the best way to answer this question is to know a little more about the historical context of Caesar's time.
Caesar was living in the time of the Republic. The Roman Republic had a constitution that emphasized parity and plurality. This basically meant that there were checks and balances in place, so that no one person would gain too much power. Rome had a hatred of kings. In fact, Rome started off as a monarchy. However, they expelled their last king and started the Republic. One of the people who did this was Brutus' great ancestor. His name was Brutus as well.
Now if we come back to the time of Caesar, Caesar was practically a king. He had gained the title of dictator for life, and he had all the military power. We can say that in a sense, he went againt Republican values. He looked like a king to many, the very thing the Roman hated.
In light of this, Brutus' slaying of Caesar can be seen as a step in restoring the Republic. For some this was a noble act.