I like to think of appendices (or supporting information, which is the same thing for a journal paper) in terms of the narrative structure of a text. The main text should contain everything that makes up the "story" of the work. In it, a reader who basically trusts that your methods are sound should find everything that they need to understand the work.
There are often, however, places where it is important to show your work, but that are not particularly interesting. If they are lengthy enough that they start feeling like a major detour in the flow of the narrative, then they are a good candidate for moving to an appendix.
Some examples from my own recent papers:
- Theorem and proof sketch in main text, boring exhaustive proof with lots of slightly different cases in appendix.
- Graph summarizing results plus an example of result detail in main text, all the rest of the results in appendix.
- Data from method presented in main text, data showing that plausible alternatives didn't work in appendix.
- Intuitive description of method and key mathematical concepts in main text, exhaustive mathematical details in appendix.
Exactly where to draw the line is somewhat subjective, but fortunately doesn't matter all that much unless you are dealing with format or length restrictions.