Consider the following phrase.
- John and Jane's house (1)
The apostrophe-s signals communication of the idea of possession. This is not simply attached to Jane, but distributed to John as well. In fact, it is a kind of abbreviation or linguistic convenience for
- John's and Jane's house (2)
which is the way such phrases are formed in inflected languages, and were formed in English when it was inflected too. So our original phrase means
- John-and-Jane's house (3), not
- John and Jane's-house.
This is why linguists consider that apostrophe-s is not merely an inflectional form of English nouns, but more a clitic—an independent linguistic element that "attaches" to regular words.
In (1), (2) and (3) above we see an example of the idea of possession being distributed to two possessors. Distribution does not have to be limited to only two possessors, it can be extended to many. The normal English word for this is their.
- their house (4)
In simple uses of the word their we might not actually be able to "see" all the possessors, but the idea is still (normally) distributive—whoever "they" may be, each has a share in the possession. Each, every and any are common signals of distribution in English.
In fact, it is this distributive aspect of the word their in English that explains the mystery of the so-called "singular" they. Although most English speakers are only aware of wanting to communicate that there are many possessors when using their, and so think of it as plural, the concept is actually more ambiguous than many native speakers realise. This becomes clear when English speakers whose usage recognises the difference encounter English speakers whose usage blurs the distinction. They discover that they are not "speaking the same language".