They’re is the short form of they are:

My parents have gone on holiday and they’re in France today.
When students like a teacher, they’re more likely to do well in the subject he or she teaches.

Their is a possessive word, just like its or my:

My children always leave their toys all over the place.
The dogs ran towards their master.

There is an adverb of place; it means in that place. Think of it as an answer to the question “where?”. Here are some sample sentences:

We didn’t want to go there, but we had to.
Why did you put my book there?

Here’s a sentence with all three words; note how they’re (!) used:

They’re there, and all their friends are with them.

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