Short version: Tomodachi Life is basically Animal Crossing with the furries replaced by Miis.
Long version: It’s a kinda-sorta Sims-like game with a dash of AC. You make or import Miis into this island town and just kinda help them out with daily problems, such as helping them sneeze or buying them clothes. Wacky things are capable of happening in the process, like weird romances (such as Hideo Kojima falling for Yukiko Amagi), or one of your Miis dreaming about being seaweed, or spontaneous barbecues. It’s a game that, on paper, doesn’t seem like a thing that’d keep one interested for many days, but somehow, SOMEHOW it just…works.
It’s worth getting if you like life-sim sort of stuff. Or just want to mess around with Miis.