You may want to use your real NAND for Mii, Wiimote settings, Internet settings, but only if you don't have it set correctly in your EmuNAND. For example, you create a clean EmuNAND with modmii, you want to play Mario kart using EmuNAND Save, but your Mii are on your Wii.
You can also just set "Partial" without creating an EmuNAND or dumping your NAND, in that case only the save path will be created on SD card, and there won't be any Wii settings, or Mii located on your SD Card. in that case you need to use "partial" mode if you didn't create a Full NAND.
If you just dumped your RealNAND, then all the settings are fine and there's no need to use the real NAND.
If you need to, in the Settings > Features, you can copy your Settings (SYSCONF) and Miis from RealNAND to EmuNAND.
That's only for Wii games.
like maxternal explained, there are Full (every access to NAND are redirected to EmuNAND) or Partial (only the save paths are redirected to EmuNAND).
For channels installed on EmuNAND, it should always be set to "full", as everything is installed on the EmuNAND, not only the savefile. So you should let the cIOS redirect everything to EmuNAND : saves, channels data and Shared Data (libraries for wii games installed only once in a single folder but used by all Titles).