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This is residence that is established under the terms of a double tax treaty - as opposed to under domestic law. It can apply in a number of cases but especially to the cases of deal residents (ie resident in two countries at the same time).

The treaty will then outline the rules that should be followed to assess which country you are resident in and this will then apply when you're interpreting the treaty (eg for employmenr income, pensions etc). This won't affect your domestic filing position and therefore even if you're treaty resident overseas you'll still be resident in your home country for domestic law purposes.

 Check out this article on treaty residence:

What is treaty residence and how to use it