A surprising number of people confuse the adverb there and the possessive pronoun their.

There is no excuse for this; the words are quite distinct in meaning, even though they sound alike.  There is an adverb of place:  "Where should I put this table?"  "Put it over there.  No, don't put it here; put it there."  The other use of there is as an expletive used to introduce a clause or a sentence:  "There is a monster lurking in the woods."  (Stylistically, sentences beginning with There + a form of to be are often indirect and can be stated more directly:  "A monster is lurking in the woods.")

Their is the possessive form of the pronoun they.  It is formed by changing the y in the nominative pronoun to ir.  The ideas that they have = their ideas:  "Their ideas are worth considering."  The homework belonging to them = their homework:  "Students should turn in their homework at the beginning of class."

They're is a contraction for "they are"; it has no other use or meaning:  "They're going to be late."