Watch the Big Bang TV show where Prof. Sheldon Cooper, to comfort someone, pats their head and says "There There" as the laugh track laughs away. Not even sure what that's supposed to mean. For Sheldon "there there" was a space filler, something to say when you don't know what to say. Same as when the Brits say "here here" or are they saying "hear hear"?
Or where have you been? Answer: Here and there. There is a place. In spanish it's aqui and alli,
Or we're asked "where is it?" and we say "over there" as you point across the room.
Or you greet someone, "Hi there" the "there" part seems to be meaningless, although maybe it means you are saying hi to someone who is almost here but still over there a little bit. In Spanish though, "Hi there" is just hola, not hola alli.
there is a place, not here, not too close, but "over there" some place not so close, either just a specific place not mentioned directly or a non-specific unknown place.
their is a violation of the rule "i before e, except after c" Apparently someone didn't follow the spelling rules when they came up with "their." It's part of the PC pronouns now to replace her or his, as they want gender neutral language, like the Finnish and the Philippine language Tagalog. Yet "their" does have "her" in it. just with an extra t and i mixed in. You don't know if they're a boy or girl so you say "their" property not his or hers. They're named with a unisex name, like Terry. So you are stuck on how to talk about them, so you refer to them in the plural since we don't have gender specific pronouns for the plural, just the singular.
they're is not allowed in formal writing. they don't like contractions. It's like slurring your words as if you were drunk or high on drugs. But we do it when sober. The peasants never followed the King's English. In Spanish the peasant were more obedient and followed the King's Spanish even to the point of mispronouncing a letter if the King had a lisp and pronounced d as th.
they're is two words in one. A real two-fer, Like Bill Clinton said when he was running for president. You get him and Hillary, a "two-fer" Buy one get one free. A real deal. They are becomes they're, sounding just like their and there, but never the twain shall meet otherwise. A rose by any other name is still a rose, but the sound of "thay-rrr" is very different depending on how you spell it. Even the one word versions, their and there, usually have two syllables: a "thay" sound and an "er" sound, "air" tends to be one syllable, but stick a "th" in front and thair just needs a 2nd syllable. Sort of like rhythm which has only one vowel, so you'd expect one syllable, but you get two.