They’re is a contraction joining they and are. The apostrophe has nothing to do with a possessive, but simply takes the place of the missing “a” when you combine the two words (such as didn’t).
So if you can write they are for a situation, then you can write they’re instead.
Their means belonging to them, whoever they are. Their friends, their boots, their thoughts. We can never say they are boots unless you are calling those people boots. If they own boots, we would say their boots.
There used to be spelled correctly almost all of the time. Now it’s in the same danger as those other two words that sound like it. There indicates a direction: “I put it over there, next to the couch.” But you already knew that.