This means that whilst a piece of software is running, everything seen on the screen comes from that software, and not from any operating system or firmware.
This includes the home menu (a menu of uniform appearance that appears when the home button is pressed in any piece of official Wii software), and any error messages that might appear.
However, if homebrew is used to forcefully install or run a piece of software when the required IOS does not exist, the user is brought back to the system menu.
Nintendo created this system so that new updates wouldn't unintentionally break compatibility with older games, but it does have the side effect that it uses up space on the Wii's internal NAND Flash memory.
Therefore, the version number reported by the Wii is actually only the version number of the System Menu.
This is why some updates do not result in a change of the version number: the System Menu itself is not updated, only (for example) IOSes and channels.
As a side effect, this means it is impossible for Nintendo to implement any functions that would affect the games themselves, for example an in-game system menu (similar to the Xbox 360's in-game Dashboard or the PS3's in-game XMB).