The word "their" is used to mean something that belongs to a group of people. see the examples:
Where is their car?Look at their dirty shoes.Their marks were poor.
The word 'they're' is a shortened version of 'they are'. See the following sentences:
They are going to the park.I think, they are a bunch of idiots.
'There' is used to show a place.
I saw the thief over there.Let us search over there.
'There' is also used to mean something that exists: There are three chairs in the room.There is no place for us to sit.There is no shortcut to success.