A bike with an extra long extension behind the seat so that a much longer rack can be installed allowing for a lot more cargo and seats for 2+ children or even an adult. There a variety of long-tails and accessories for different kinds of cargo. Long-tails are typically more affordable than box bikes and has components that are readily available in North American bike shops. They usually cannot carry as much stuff as box bikes.
Made popular first by the Xtracycle add-on for mountain bikes, but now a bunch of companies making dedicated bikes, including Yuba, Surly, Salsa and Kona. Surly and Salsa even have fat bike versions of the long-tail to make them useful in even more climates.