Their is simply the posessive adjective (or determiner), as seen below:
As you can see, we use possessive adjectives (or determiners) with a noun.
This is quite simply a contraction:
THEY + ARE
As you can see, they apostrophe (') substitutes the 'a' in the verb ARE. So 'they're' is actually a subject + a verb (they+are.) Here are some examples:
They're (they+are)almost ready to go!
They're (they+are) visiting us in August.
They're (they+are) the new champions.
This is what is referred to in grammar as a "dummy subject." What is a "dummy subject?" Well, in English there MUST be a subject and a verb. So, when we don't have a specific verb (my mother, your teacher, his brother, Mary, John, Xander...etc.) There serves as a general verb. Here are a few examples:
There is some chocolate cake left if you want some. (present)
There was a big storm outside, so take your umbrella. (past)
There are mosquitos in the room!...It keeps biting me! (present)
There will be consequences for your actions. (future)
As you can see, you can use there with the past, present or future.
I hope this clears up your doubts. If you happen to still have some, leave questions or comments below.