What Does THERE Mean?

There can be used in a couple of ways. As an adverb, there is the exact opposite of the word here and means “at that place”:

He asked me to go there and check on his fish while he’s away.
There is also often used as a pronoun. In that case, its role is usually to introduce a word or a clause:

There is something strange going on with Sydney today.

What Does THEIR Mean?

Their is the third-person plural possessive pronoun:

All of those kids with their contagious laughter really made my day.
They didn’t want to see all of their hard work go to waste.

What Does THEY'RE Mean?

They’re is what you get when you contract “they are” or “they were.” It’s the same kind of thing that happens when you contract “we are” into “we’re,” or “you are” into “you’re”:

They’re going to a party tomorrow.
You should meet my work friends; they’re a real hoot.