If you want the dictionary definition, just double click on any word.

There can be used as an adjective of place:-
For example: "The car is over there in the car park."

There can also be used as the introductory subject in sentences:-
For example: "There are some grammar pages on this web site."

They're is the contraction of "they are".
For example: "They're always surfing the Internet."

Their is a possessive pronoun like "her" or "our" indicating that something belongs to more than one person, not including yourself.
For example: "Have they done their homework?"

Example: "There's a large family in this town. Look they're over there by their car."

!Note - If you've written "they're," ask yourself whether you can substitute "they are." If not, you've made a mistake. There" has "here" inside it to remind you it refers to a place, while "their" has "heir" buried in it to remind you that it has to do with possession.