's can mean two things.
It can be an abbreviated of is.
It's a rock. = It is a rock.
The wall's tall. = The wall is tall.
The garden's green. = The garden is green.
If there is an article or an adjective after 's, it's always this form.
's can also indicate possession:
John's cat = The cat the John has
The king's crown = The crown the king has
When there is a noun without an article directly afterwards, this is the meaning it usually takes. In third person plural (when an article is not compulsory), you have to use your judgement.
The cat's fur = the fur the cat has.
If you're talking about cats in plural, then there is already is an 's' there anyway. When there already is an 's', you at the apostrophe after the 's'.
The cats' fur = the fur the cats have
The leaves' colour = The colour of the leaves