I read in a relatively older book (from 1967) that this form, the third person plural, is actually ambiguous. It can mean both "Their book" and "Their books". I wonder if this is still true today, or the ambiguity has been resolved in general use as described below. Let me paraphrase from the book (Elementary Turkish), applied to this example:
The word "kitapları" may be the singular (kitap) plus the third plural possessive suffix (-lari) required by the first member (onların), i.e. "kitap-ları". If so, the words "onların kitapları"mean "(the) book of them" (their book).
But the word "kitapları" may also be the plural (kitaplar) plus the third plural possessive suffix (-ları) required by the first member (onların). Two plural suffixes never come on the same noun: hence the logically expectable "kitap-lar-ları" does not occur.
Thus "Onların kitapları" may mean both
"(the) book of them" (their book)
"(the) books of them" (their books)
The ambiguity may be resolved in one of two ways: the context is left to show whether one or more books is intended; a singular possessive suffix is given the second member, even though the first member is plural: "Onlarin kitabı", "(the) book of them" (their book), in which "book" is indubitably singular.
In the introductory text below the 3 tiles with the Possessives lessons, it says that the 3rd person plural possessive suffix is the same as for the 3rd person singular. An example is given for "kedi", which in both cases is "kedisi". But, from what I had learned elsewhere thus far I understood it should be "kedileri", and the sentence above confirms that too: 3rd person plural is -leri or -lari. So why the difference in the introductory text?
I was wondering the same thing. I feel like I'm missing something, because most other learners do seem to be aware that the 3rd person plural possessive suffix is sometimes -leri / -ları and sometimes -(s)I, but I can't find info about this in the Tips & Notes, nor the grammar portal. Was this explained elsewhere?