What kind of music should be used will depend upon the nature of the video and its purpose. There are, however, some things that will be common with all music for videos, especially when that music is employed to great effect.
When it comes to the sound design of any video, music plays a critical role. More than any other form of art, music has the greatest capability of producing an emotional reaction in its audience in the shortest amount of time. For example, one will often hear sad music in commercials that implore their viewers to make donations to one particular cause or another.
In order for music to be used effectively in video, though, a few things need to be done. For one, a film editor will want to make sure that the piece of music being used is cut to length, beginning and ending where the filmed content does. For example, when you hear a piece of popular music in a commercial or in a movie, you will often find that certain bits of a particular song have been excised and other parts blended together to fit the length of the commercial or scene.
In other cases, the filmed content will be matched to a particular piece of music. This is the case, most notably, with music videos. Here, the action that is occurring on screen will be rhythmically matched to the song itself. This is accomplished in both the filming of the particular video and in the editing of that video. If, for example, the video features dancers, they will be filmed dancing to the song that will appear in the video. Likewise, a film editor will make cuts and transitions in the video that match the transitions in the piece of music itself.
Whatever the case, background music is an integral part of making any video, and a video without music will hardly be a video at all. Therefore, the sound designer in charge of any given video will want to make sure that the music being used is employed to its greatest effect along the lines outlined above.