Brutus's inner conflict has to do with his personal feelings about Caesar and his misgivings about Caesar's ambitions. Brutus loves Caesar and feel correctly that Caesar feels the same way about him. Yet Brutus feels that he has a responsibility toward Rome because without his participation in the plot against Caesar the assassination would probably not be carried out, and if it were carried out successfully, then the government that took power afterward might be a tyrannical and corrupt one. Brutus, on the one hand, feels he should take part in the proposed assassination of Caesar, but, on the other hand, he doesn't want to kill his friend, a man who has never done him any harm but has always treated him generouosly.
Brutus' conflict is spelled out in the long soliloquy in Act 2, Scene 1, beginning with the words
It must be by his death. And for my part
I know no personal cause to spurn at him,
But for the general.
He is weighing his personal feelings against the general good.