This quote is powerful because it really demonstrates that Brutus is a man of integrity and honor. Although one might not think of murdering someone as being an act of integrity or honor, his reasoning shows that his intentions behind the murder were good.
Brutus was good friends with Caesar and it was not easy for him to decide to be part of the conspiracy to kill him. He did so, however, because he recognized that his friend posed a great threat to Rome and in order to save Rome, Caesar's death was a necessary evil. When he says that he loved Rome more, he is also saying that the needs of the many were more important than his needs or the needs of Caesar. So, as difficult as it was for him to kill Caesar, he felt that the morally right thing to do for his city was to kill him.
This passage also demonstrates how hard this choice was for Brutus and reminds us again of his own inner conflict.
This line is spoken by Brutus. It is found very early in Act III, Scene 2. What is going on is that Brutus is going to address a crowd of Romans. They are going to want to hear what he has to say -- why he and the conspirators decided to kill Caesar. The actual line is
Not that I loved Caesar less, but that I loved
What he is saying in the line you cite is that he was friends with Caesar. He is trying to tell the people that he loved Caesar, but that Caesar was bad for Rome. Because Caesar was bad for Rome, and because Brutus loved Rome more than he loved Caesar, Brutus decided that it was necessary to kill Caesar.
So he is saying that he didn't really want to kill his friend, but he had to do it for patriotic reasons.