I think it's a direct translation of how japanese talk about 連濁: てんてんをつける/てんてんがつく. てんてん is the second meaning of 点々 here and it's just the two dots 「゛」that you attach to a lot of kana (ひ -> び, と -> ど, つ -> づ, etc). Never heard of that expression before but it's a interesting way to introduce the concept. And more useful than knowing it's technically called 連濁 since not all japanese know the technical term but they will understand if you say てんてんをつける or てんてんがつく. I always get frustrated when I'm talking with japanese with those kind of technical term and they don't know it. I feel like I'm constantly showing off :v
As to where it happens, well, it happens in compound words. For the "when" tho, there are no absolute rule but a lot of pseudo rule. For me, I think it's faster to just learn the word where it happens directly one by one. But if you want to know more, you can just type rendaku on google, you will have more result that way in english ironically.
Also 連濁 is literaly 連 (connect) + 濁点 ・濁音 depending on how you want to interpret it. 濁点 being the two dots 「゛」, so it's more or less the same as "Ten-Ten hooking" =p. And 濁音 is all the kana with a 濁点 (ガ・ザ・ダ・バ行音).
PS: Nothing to do with question but I just found an interesting thing about the kanji 濁 while looking at the JP definition in the dictionary. One of its meaning is 汚くなる ("becoming dirty"). And Japanese often think as 濁音 as rough, coarse, unpleasant sounds. Especially ぞ, ぜ for example (the particule ones often associated with yankee speech). Never though that perception would show even in the kanji meaning x)
There's rendaku, where that commonly happens. There is a sort of general guideline for that.
There are also characters that used to exist, but are not common, which have tenten. You don't have to worry about those, but basically the point is there's a change in consonant pronunciation based on these diacritical marks.
