All right, often times I see people using either there or their for any two or even all three words at the same time. Much like the differences in then and than, many people just don't seem to understand the differences of these three words.

First we'll start with the easiest of the three. There. There indicates a place the speaker or narrator is talking about.

"We need to get there as soon as possible."

Get it? Got it? Good.

Now, onto the possessive pronoun known as their.

Their is a word that speaks of something belonging to them which is a form of they. They refers to two or more people other than oneself or a group (we) that oneself belongs to.

"The neighbors' cat was tearing up their flower garden."

Their refers to the neighbors at the beginning of the sentence. Their can also stand alone in reference to an aforementioned group of two or more people in a separate sentence.

"I love Fred and Sandy's cat. It is white with black spots. Unfortunately for them, it also likes to dig in their garden."

Often when reading stories here and on so many other sites, I have noticed that people use our next word in place of their. They're, however, is a conjunction of two separate words where as their and there are singular words.

They're is the conjunction of two words: they and are. Thus the word they're means they are.

"They are going to the market." can be replaced with "They're going to the market." when conjunctions are acceptable.

So, let's get the basic overview and wrap up.

There--indicates a place

Their--belonging to them

They're--they are

A place, a thing, and an action may sound the same, but they are spelled differently to show the difference.