The Hills Big Band uses a band format that has been around for a century.
The format of a standard Big Band is a rhythm section (piano, bass, drums and guitar) with brass and woodwind instruments (four trumpets, four trombones and five saxophones). The addition of one or two vocalists allows a Big Band to include vocal repertoire. The format sometimes includes orchestral instruments such as flute, clarinet, french horn or even a small string ensemble, and is also known as a "Jazz Orchestra".
Big Bands first came into prominence playing dance music in 1920s in USA, and their popularity soared during the "Swing Era" of the late 1930s and early 1940s. They were perfect for the burgeoning dance craze that swept the nation and spread to Europe with the help of LP recordings and radio. Big Bands moved into Hollywood to supply music for the motion picture industry, and movies were even made about Big Bands.
Although it seems that the Big Band might have had its day with the end of World War 2, the format is far from extinct! Schools and universities use the Big Band format to teach music performance and arranging to students. Big Band music features prominently in many TV shows. Movies have buoyed the popularity of old recordings of well-known artists, as well as introducing new music, keeping the format and its associated musical genres popular and relevant.
You can find more about famous Big Bands and the musicians that played in them on Wikipedia - "Big Band".