Don’t be confused by the fact that ’s is used for the possessive of nouns (the book’s cover, John’s coat). It behaves differently because it is a pronoun: think of its as the partner of the possessive pronoun his (‘of him’) – which, as you know, also has no apostrophe.
Its means ‘belonging to it’:
Its colour is bright green.
You can’t tell a book by its cover.
It’s is short for it is or it has:
It’s never happened before.
It’s ruined everything.
©2015 Baxter Publishing, Hilversum, The Netherlands