The question should be:
What is the difference between "This is my mom and dad" and "They are my mom and dad"?
The answer is it's about usage. In the first instance your parents are, presumably, in the room and nearby. You are introducing them to somebody, and you say: "This is my mom and dad." In the second instance somebody has said, perhaps: "Who are Debbie Simpson and Allen Simpson?" and you reply: "They are my mom and dad."
Don't use "this" with plural nouns, but "mom" and "dad" are not plural nouns.