Why get a round cutting board? Well, there is an aesthetic reason: you may find they look nicer than the usual rectangular boards. Similarly, a round board could also be used as a serving tray for cheese and crackers (sort of like a paddle board or cheese board), for serving pizza, or even as a cake stand. It could also be used as a sort of size-guide when making pizza, dosas, or pita bread.
Round plastic cutting boards:
Round plastic cutting board pictured: Excellante Polyethylene Round Cutting Board, Size: 1-1/2 by 14-Inch
The disadvantage of a round board is that it can be harder to store.