These terms have the same pronunciation but very different meanings.

Their ( belonging to them ): is a plural possessive adjective for people or things, similar to the singular his, her and its. Example :
1. Gopi must have come. This is his car.
2. The girl broke her leg.

There ( not here ): is an adverb of place, basically the opposite of "here". We use it in sentences like these. Example :
1. I went there last week.
2. Shall we sit here or there?

they're ( they are ): is a contraction (short form) of "they are". Example :
1. They're happy.
2. They're playing football.