What is a DJ license?

There is no such thing as a DJ license; DJ's do not require a certain degree or certificate in order to pursue their trade. This does not prevent DJ's from having licenses to play the music they use during their sets -- but this would fall under music copyright law, similar to the laws that businesses must adhere to when playing music for employees/customers over speakers. Most music that DJ's are found utilizing in these events have already made deals or pay royalties to allow their music to be performed in public settings, in most countries in the world.