The Everett interpretation isn't very popular in scientific circles. That being said, what 'splits off' is that every superposition of states which collapses into an eigenstate, i.e. a single determined state of some observable, is played out in some world. So for instance, if you have a superposition of spin states in some system, two electrons, you measure one and see it's spin up, infer the other must be spin down, in some other universe you measured spin down.
By the way, every time you are trying to learn about quantum mechanics and people are talking about themselves doing measurements, you can just as well replace that with any physical interaction that causes decoherence. It doesn't have to be a literal measurement by a person.