Swing music, or simply Swing, is a form of American music that developed in the early 1930s and became a distinctive style by 1940. Swing uses a strong rhythm section of double bass and drums as the anchor for a lead section of brass instruments such as trumpets and trombones, woodwinds including saxophones and clarinets, and sometimes stringed instruments such as violin and guitar, medium to fast tempos, and a “lilting” swing time rhythm. The name swing came from the phrase ‘swing feel’ where the emphasis is on the off–beat or weaker pulse in the music (unlike classical music). Swing bands usually featured soloists who would improvise on the melody over the arrangement.

The danceable swing style of big bands and bandleaders such as Benny Goodman was the dominant form of American popular music from 1935 to 1946, a period known as the Swing Era.

Source: Wikipedia

Some swing dance music examples (both more modern and older!)

This one is a classic:

This one is more modern, from 2009 by Carsie Blanton.

And a few more:

Some electro swing!