Don’t confuse they’re, there, and their. A mistake involving these makes my head spin…and the heads of many others.
They’re is a shortened version of they are. (The apostrophe replaces the letter a.) Only use they’re if you can substitute it with they are.
Their is used to show possession. It is just like my, your, his, her, its, and our. (These are called possessive adjectives.) Here is a little trick: use the word our instead of their. If the sentence still makes sense, then their is almost certainly correct. This trick works because our and their are both possessive adjectives used for plurals.
The word there is similar to the word here in that it represents a place. It has two main uses: (1) it is a specified place, and (2) it is an unspecified place. Also, the word there can be used to show that something exists.