Their is the correct spelling of the word. Thier is incorrect and not a word in English.
Their is a possessive pronoun that means that a group of people (They) own something.
That is their house.
Do you want to drive their car?
Thier is a very common mistake in English. People often make spelling mistakes in English because the position of “i” and “e” can often confuse people.
In this case, the “i” should come after the “e”. There is a famous rhyme in English that goes like this, “i before e except after c”. There are so many exceptions to this rule that it shouldn’t even be a rule.
Words like “their” can be difficult to spell because most words do follow the pattern “ie” in English.
The correct spelling is “their” and not “thier”.