Acquaintances are Miis that know each other, but are not friends. This is the default of all relationships when a Mii is first created unless it was born on the island. They can become friends potentially if they have an orange friendship problem or when the game is turned off. If Miis fail to make up after a fight and don't reconcile, they might get removed from each other's relationship charts, once again becoming acquaintances.
Miis that are acquaintances have no opinions on the other Mii, even if they did before getting removed from each other's friendship charts.