A raid card is a storage controller which has it's own dedicated hardware for creating raid arrays and it has a microprocessor for it's own data calculations (
here's an example. Most storage controllers, with raid support, that are integrated on motherboard are so called software raid type. They don't have the actual hardware and the main cpu of the system does all the data processing. Dedicated raid cards with their own processor are a lot more powerfull, but are also usually expensive.
Those storage controllers on that Asrock board are there to support more SATA ports (you would only have 6 SATA ports without the additional controllers, which add another 6 to make it 12 in total).
For home NAS you are propably fine without any dedicated hardware raid card. You can easily setup a NAS with multiple harddrives with raid type functionality using
Free NAS for example.