The homonyms there, their, and they're are frequently confused in English writing. Although readers will be able to understand the intention most of the time, learning how to use them correctly can prevent confusion. The words actually have entirely different meanings, since one can be used in multiple ways, depending on the context, one is a contraction, and one is a pronoun.
The word “there” can appear as a pronoun, as in “over there,” an adverb, like “she went there,” as an interjection, or, in some English dialects, as an adjective, such as “that man there.” It can be used to indicate directional movement away from a location, as when someone is told to “go over there,” to clarify a sentence such as “the nail's there,” or in reference to an issue, such as “I agree with him there.” A useful way to think of this word is that it contains another place, “here.” Often, “here” can replace “there” in a sentence, indicating that “there” is being used to indicate a location in time or space.
You may also encounter “there's,” a contraction of “there is.” In formal written English, both words should be written out, and remember not to confuse it with “theirs,” a possessive pronoun. As with all contractions, if you are uncertain about the use of the word, stop and decide whether “there is” can replace “there's” in a sentence. “There's no place like home” is correct; “theirs no place like home” is not. On the flip side, the boat is theirs, not there's.
”Their” is a possessive pronoun. In a phrase like “Susan and Bill's car,” the word could be used to replace the possessive proper noun construction to make a new phrase: “their car.” It is related to “they,” another pronoun indicating a group of people. You may also see their in the form of sentences like “that dog is theirs.”
”They're” is actually a contraction of “they are,” a phrase which contains a pronoun and a verb. It is more commonly used in spoken rather than written English, when one wants to say “they're going to the store,” for example. In written English, “they are” should always be able to replace “they're.” In the phrase “they're going to their house, over there,” you can see all three words in use.