This song has a very deep meaning. It is about love. Mariah Carey is expressing how important it is to have people you love by your side during the holiday season, as expressed when she says: "I don't want a lot for Christmas, there is just one thing I need,"
She is explaining the importance of friends and family over material belongings "Santa Claus won't make me happy with a toy on Christmas day."
However, specifically, she is speaking about a love interest when she says "All I want for Christmas is you/ You, baby". This is reinforced when she says "And I'm gonna keep on waiting/ Underneath the mistletoe" Mistletoe is a plant, people hang up and it is a tradition that if two people are under it together they kiss. She is implying that she would like to kiss her love interest.