In Ancient Rome there was huge emphasis on social influence, or dignitas. One way to accrue this social currency was through establishing many client-patron relationships, giving clients things such as loans in exchange for their political backing of the patron. When Caesar was fighting his civil war against Pompey, he (at first) offered clemency, or forgiveness, to his enemies. This probably wasn't so much an act of kindness from the bottom of his heart, but rather a way to gain even greater dignitas because these people, in exchange for Caesar's clemency, would be obligated to support him politically. The enemies, by way of accepting clemency, would be implicitly admitting that they did something wrong that needed to be 'forgiven'. Cato the Younger, for example, killed himself to avoid living in a world where he had to be forgiven by Caesar and be indebted to him.

Another reason for his sparing Brutus and others is simply because he did not want to be seen as another Sulla. Clemency is essentially the opposite of proscription, where you basically put a public bounty on your political enemies and anyone else who could be considered a threat. This eased some anxiety from the Romans, because the last thing they wanted was another Sulla.

Did Caesar's relationship with Servilia have anything to do with him sparing Brutus?