IOS exploits are bugs in the way that the Wii's internal firmware handles data. For 100% homebrew to execute, an IOS exploit is needed only to install new versions of the Homebrew Channel. Homebrew that accesses game savedata generally requires an IOS exploit to function, as well as homebrew that installs a modified IOS.
Most homebrew users will not need to apply these directly, they are only of use to educated programmers that understand the risk inherent in modified system firmware. If you have homebrew that utilizes IOS exploits, make sure you understand the risks and protect yourself if you can.