What do software publishers mean by the term: "royalty-free", when it comes to graphics and midi/sound files?

Answer 1

It means that you can use them in your applications or projects, and you don't have to pay the creator of the graphic, music, or sound file anything to use it.

Answer 2

That means when you use those properties for profit, you don't need to pay royalties. You usually only required to pay the initial/one time only fee (eg. when you purchase the property).