their OR there OR they're?

These three terms have the same pronunciation but very different meanings.

their = belonging to them
there = not here
they're = they are

their

The word their is a plural possessive adjective for people or things, similar to the singular his, her and its:

Here are some example sentences:

there

The word there is an adverb of place, basically the opposite of "here". We use it in sentences like these:

We also use there in phrases like:

Note that in speech "there is" is often contracted to "there's":
  • There's a man at the door.
  • Do you think there's any possibility he'll come?

they're

This is a contraction (short form) of "they are". Look at these examples:

Note that in this contraction, "are" can be a main verb or an auxiliary verb:
  • They're here (they are here - "are" = main verb)
  • They're watching TV (they are watching - "are" = auxiliary verb)
Here is a sentence that contains all three terms:
  • They're living in their new house over there.