A virtual circuit-breaker is a relay (solid-state or otherwise) where the current going through it is monitored by a computer of some sort. When the computer sees too much current going through it, the computer trips the relay open. (Think of it as 'active CB' versus 'passive CB'.)
The engineer/pilot can access the computer to find out which CBs have been tripped by the system, and can try to get the system to close them again, just like resetting a real CB.
Advantage 1 - you can guarantee that the CB will trip at the target amperage, a real CB will often have a large error in its trip amperage.
Advantage 2 - real CBs have to be mounted where they're accessible to the crew, virtual CBs can be mounted anywhere that's convenient for the systems design engineer.