The words their, there, they're sound the same but have different meanings and spellings. Why do their, there, they're sound the same even though they are completely different words?
The answer is simple: their, there, they're are homophones of the English language.
Used as a modifier before a noun: their accomplishments; their home town.
Usage Problem His, her, or its: "It is fatal for anyone who writes to think of their sex” ( Virginia Woolf). See Usage Notes at he1, they.
At or in that place: sit over there.
To, into, or toward that place: wouldn't go there again.
At that stage, moment, or point: Stop there before you make any more mistakes.
In that matter: I can't agree with him there.
Contraction of they are.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.