It seems that Hello Kitty has decided to move to Big City, but she doesn't really know anyone in the area and is living on the lowest floor of her apartment complex with dreams of someday living in the top-floor penthouse. So your goals in Big City Dreams involve making new friends, helping others and earning points to help you rise in the apartment complex.
In order to do this, you will guide Kitty around the city meeting various people (including some familiar faces) and helping them in mini-games. These mini-games include actions like making sushi, washing cars, fishing, using a crane to pick up toys and taking pictures while on a boat (think Pokemon Snap). Doing so will earn you friendship points which you can use to buy plush animals for your apartment (or to give to friends), clothes for Kitty or themes for the apartment itself.