From Nookipedia, the Animal Crossing wiki
The parents of the player are unseen characters present throughout the Animal Crossing series. Mom will occasionally write letters, in addition to one shortly after moving to town and another on Mother's Day, while Dad writes only on Father's Day. In Animal Crossing: New Leaf, however, the father sends the player more letters, but not as often as Mom. They are the only humans apart from the players and in television programs referenced in the series.
In all Animal Crossing games, the player will frequently receive in-game letters from Mom, purportedly the character's mother. Letters from Mom usually contain a small anecdote about life in the character's home prior to moving into the town; these anecdotes usually concern certain memories of the player that she has, a tale relating to "Dad", or a few words of wisdom or guidance.
Mom will also occasionally send gifts in the mail, on the player's birthday, and on New Year's day. Mom also sends non-native fruit, acorns, and mushrooms in the mail as gifts as well on random occasions, always with a relevant story attached. In Doubutsu no Mori e+, Mom sends a letter talking about a Bean Throwing Festival on February 3rd. Later, in July 7th, she will discuss the Festival of the Weaver.
Mom is never actually seen, nor is it known how or why the player came to move away from home in the first place. Outside of the letters, the player's mother is never mentioned by any other animal. It is also not possible to send letters back to Mom.
Dad is the father of the player in Animal Crossing series. He originally only wrote on Father's Day, usually saying something like "See? Your Mom isn't the only writer in the family". Like Mom, he is not seen and is a small part of the player's life. In Animal Crossing: City Folk and Animal Crossing: New Leaf, he gives the player a red carnation during Father's Day, which is the only way to obtain the special flower. In New Leaf, he has a larger role and now sends the player more letters.