Even professional writers occasionally mix up their, there, and they’re in their absentminded moments. These errors can hurt a writer’s credibility, however, so it’s important to use these words cautiously.
Their functions as an adjective. It is the possessive of they—for example:
The neighbors watch their TV very loud.
Cats get grouchy without their dinner.
Most wives love their husbands.
There functions in several ways. It can be an adverb meaning at, in, or toward that place—for example:
Steve Carlton also pitched there. [ESPN]
There is plenty of optimism in Baltimore right now. [Baltimore Sun]
There will be a lot of fuss about such principles and practices, but it won’t hold. [Guardian]
It works as an adjective used for emphasis or to indicate that something is at a certain place:
His passion for the people there is so strong he’s adopted two children from the island nation. [USA Today]
It works as a noun meaning that place:
And the lame-brained lies build from there. [ABC News]
And it works as an interjection used to express relief, satisfaction, or sympathy:
There, that’s much better.
They’re is short for they are—for example:
They’re coming over at six.
I don’t know what they’re doing, but I don’t like it.
They think they’re so special.