What is the Difference between There, Their, and They're?

Glad you asked. "There" indicates a place as in, "I live here not there." It is the opposite of "here." "Their" is the possessive of "they", as in "They live there but is isn't their house." Here you want to indicate that the house belongs to them. "They're" is a contraction of "they are", so that to say, "They're over there in their new house" means "They are over at that place in the new house that belongs to them."