There means here. E.g My puppy likes to sleep there. Same sentence, My puppy likes to sleep here. They both mean the same thing. "There" is like "here".
Their means you are talking about a person. E.g I really like their shirt. Same sentence, I really like her/his shirt. They both mean the same thing. "Their is like "her or his".
They're is short for "they are". E.g Kim likes eggs only when they're hard-boiled. Same sentence, Kim likes egg only when they are hard-boiled. They both means the same thing. "They're is like "they are".
