NAND is a type of physical memory chipset.
The Wii has this type of memory as it's internal storing space (512MB of NAND).
Think that the NAND is an internal SD Card instead of using an hard drive.
When installing a Channel, it is then installed on the NAND.
As a game has many different names depending the location/country, it is installed in a folder using its TitleID instead of its game name. (nand:/00010002/48414341/ = Mii channel)
Any Title Deleter Mod has a database including known game Titles to show the correct name instead of the folder name with the titleID.
About the dump, you can make a full copy of the NAND memory byte by byte (with Bootmii dump menu), and save it as a binary file on your SDCard or computer.
This nand.bin file is a 1:1 copy of the content of your Wii (data, save games, channels, firmware, IOS, config, message, mii, etc. all your wii content).
ShowMiiWads is a Windows program allowing you to extract the nand.bin file into files and folder structure, like if you browsed your wii memory.
Once you have all the file/folder structure on your computer, this is like if you have a Virtual Wii on your computer.
ShowMiiWads can easily install/delete wads files into that "virtual Wii" using the "ShowMiiNand" option, it can list the installed channels and gives you their names, extract banners, make them region free, etc.
(ShowMiiWads has a menu to swap between ShowMiiWads and ShowMiiNand after pointing to the virtual wii folder)
You may want to know what this "vitual Wii" may be used for?
On your PC it has no real purpose, but once on SD or USB you can fool the Wii to think that these folders are the real internal memory. This is called as "Nand emulation".
You can use homebrew which reads the wads installed in this emulated nand instead of the real nand :
Triiforce,
Mighty Channel.
You can also boot your wii fully into this emulated mode using
Sneek, showing the Wii menu with the installed channels and booting games as if it was a real wii.
The advantage of the Emulated nand and Sneek is that you can now use a really big hard drive (2TB) as your Wii available space, you can install a lot of WiiWare without running out of space. 512MB is no longer a problem