there means in that place or in that respect.

their means belonging to them.

they're is a contraction of they are.

Examples:

Correct: Please let us know if there is any way we can improve our service.

Incorrect: Please lt us know if their is any way we can improve our service.

Correct: Everyone can join in the fun and sing along to their favourite tracks.

Incorrect: Everyone can join in the fun and sing along to there favourite tracks.

Correct: They're going to move out into the country.

Incorrect: Their going to move out into the country.

Correct: Their are fourteen bright colour schemes from which to choose.

Incorrect: They're are fourteen bright colour schemes from which to choose.

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Find the answers to grammatical puzzles like this in The Grammar Cookbook!