Their - The word 'their' is a plural possessive adjective for people or things, similar to the singular his, her and its. Example :
1. Parents always want the best for their children.
2. I could hear their voices but I couldn't see them.

There - The word 'there' is an adverb of place, basically the opposite of "here". Example :
1. I went there last week.
2. Shall we sit here or there?

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