I am under the impression that we use the apostrophe to describe ownership. Someone would say "This is Jennifer's coat" to mean that the coat belongs to her, as opposed to, for instance, "Jennifers are people who enjoy arranging flowers" implying there are more than one of Jennifer.
However, I have been told that if I were to say "It's coat" I would not be saying (for instance) "The monster's coat" but rather I would be saying "It is coat".
What is the difference here? Can you explain how the apostrophe works in greater detail?