The tips and notes explain that. This is the information for nouns starting with a vowel. my, your (sing) and his don't have anything added (aside from the possessive pronoun). But the "mo" and "do" do become "m' " and "d' " (because they're in front of a vowel).
When you are saying her apple, add the h directly "a húll", our apple, their apple or your (pl) apple, add n- "ár n-úll" "bhur n-úll" "a n-úll"
I guess the dash is to differentiate eclipsed words from other words (which may be pronounced the same), and since it was more practical for some words they extended it to all (or it maybe increased reading speed because it cuts words out, so it was kept that way, or some combination of both)
The dash is probably there because many Irish nouns begin with 'n' followed by a vowel. The dash shows that the 'n' is not the first letter of a noun.
Very few native Irish nouns begin with 'h' so presumably a dash was felt to be unnecessary after a prefixed 'h'.
Anywhere you see a dash you can assume there is a reason for it, even if the reason may not be evident to you at the time of doing the exercise. It's not a random thing.