In a nutshell, Royalty Free Music refers to a type of music licensing that allows the music purchaser to pay for the music license only, and then is able to use the music for as long as they desire. Essentially you are required to only pay a one-time free to gain the legal right to use a composer's music.
The term royalty free is confusing, however, it simply means 'free of royalties'. Note that this does not mean it is free of costs! This just means that once you acquire the music, you are not required to pay royalty fees for using it.