What does it mean exactly?
In a nutshell Royalty Free Music refers to a type of music licensing that allows the purchaser to pay for the music license only once and to use the music for as long as desired.
For example you purchase a Royalty Free Music license for a video on your website. You pay one single price whether you have 100 visitors or 10,000 visitors, and whether you use the music for 1 month or 10 years. Or you purchase a TV advertising license for your new restaurant. You pay once and the commercial can play once a week or 50 times a week, for 3 months or for 5 years. You pay once and you use it for as long as you want.
The term "Royalty Free" is confusing for more reasons than one. In fact it simply means "Free of Royalty". The term is in opposition to "rights managed" licensing where the purchaser pays fees (royalties) according to the number of times it will be used as well as the size of the territory. With Rights Managed licensing or "Needle Drop" licensing you would need to pay a fee every time the music is used or as the old term expressed every time the "needle is dropped" on the record.
Royalty Free Music is NOT free!
It is "Free of Royalty" not cost free. Just like a fat free cookie is "free of fat" not free of cost. Or a "tax free" product is not free, it is just free of taxes. And yes some people may be offering their music for free - whether it is also Royalty Free or not! For example a composer may be offering you his music for free for your College film in exchange for listing his work in the credits.
Royalty Free Music is NOT Stock Music
Although most Royalty Free Music comes from Stock Music Library such as Premiumbeat.com they are not synonymous. A Stock Music Library is a music library that offers music already in stock - already made and ready to license and use. Although some people consider Stock Music negatively as cheap "canned music" it is not the case at all. You have the full range of music quality in stock music from very amateurish poorly mixed music to highly professional music tracks. Stock music is understood in opposition to "custom made" music that is created for a specific product - a film, a commercial, a TV show… Many stock music libraries offer their music on a Royalty Free basis, but other libraries prefer to offer their music with a Rights Managed model or "per usage" based on the frequency of use as well as the size of the territory.
Royalty Free Music is NOT Copyright Free music
I am not sure there is such a thing as "Copyright free" music since anyone who creates a piece of music automatically owns the Copyright for that music. The creator may not care and say that anyone can use his music for any purpose. In this case the Copyright owner is giving you the "right to copy" his music for any purpose. So it may be free to use but that does not make it free of Copyright. And this does not mean that the composer has given up his Performing Rights if his music ends up a background music on television for example. The composer as the Copyright owner may want to receive his composers royalties for the public performance of his music. Even the recordings of Public Domain music are not Copyright Free. The composition may be Copyright Free but not the actual sound recording (also called the Master). You can read an excellent text about Copyright and Public Domain music at PDInfo.com.