The trio of their, they’re, and there can be traps to catch the unwary, but — with a bit of patience — they’re easy to navigate.
Their is a possessive word, showing ownership: Jack and Jill went up their hill.
They’re is a contraction of the words they are: They’re going up their hill. As with all contractions, it’s useful to read over the sentence and mentally replace the apostrophe with the missing letters to verify that you’re using the correct word. Contractions should be avoided in academic and formal writing.
There refers to a place or a time: The hill over there. There once was a hill here.