In a nutshell, accepting the risk instead of paying for someone else to take the risk.This might be a dumb question, but what does self-insuring entail?
Accepting the risk = paying for the repair or replacement or doing without the thing if something goes wrong with it.
Some people make a separate account or column in their budget for it. Or for some types - cars, for example. But that is just to help people see where their money is and what it is doing. It isn't needed for the concept.
Edit - I type slow. This isn't instead of gtaus' explanation.