There:
* Location: "I left my keys there on the table."
* Existence: "There are three apples in the basket."
* Introducing a new topic: "There is a new restaurant opening downtown."
Their:
* Possession: "They brought their dog to the park."
* Ownership: "The students finished their homework."
* Referring to a group: "The team celebrated their victory."
Remember:
* There refers to a place or the existence of something.
* Their shows possession or ownership, usually referring to a group of people.