Whenever an original piece of music is composed, many of those who write it have a particular set of instruments in mind. While most artists see a vision in their mind, a musical composer hears the notes of an instrument. They write down their notes, and they often specify which instruments are to play each part of the music. Many pieces are scored for several different instruments, so band leaders and conductors know exactly how to assign the work to their own musicians.
As time passes, new ways to play a piece of music can be found by musicians who are searching for a new way to please audiences. When they arrange a piece of music, they are essentially reassigning parts of it to different instruments than the composer called for in their work. If the piece has words to be sung, they can change the notes to match the voice of the person singing.
Some musical arrangements have only part of the music rewritten, and it is often done to keep the melodic line exactly the same. A popular piece, with the background instrumental parts rewritten, will sound essentially the same while it also adds a different depth to the piece. Base lines for compositions are often the place where musical arrangements are done to update and refresh an old favorite.
One of the ways composers arrange their own music is to write variations on a theme, and this has always been a popular way for them to help the audience see how their music transcends one instrument. They often write a short piece, and then they rearrange it for different instruments. There is a very short pause between the pieces, and it is meant only to give audiences a chance to realize a new variation will begin shortly.