What is the difference between their, there, and they're?

Their, there, and they're are homophones.  Homophones are words that sound similar but have different meanings and spellings.  Their is a possessive pronoun, as in "their bicycle is green".  They're is a contraction of "they are", as in "they're going to the game tomorrow".  There is an adjective, as in "she is always there for her friends".  There can also be used as a noun, as in "stay out of there", or as an adverb, as in "stop over there".