Term for a version of a song that has been
edited to make it more suitable for
radio airplay.
The most common reason for doing this is that the length of the original album track would be unsuited for airplay on most radio stations, i.e. longer than about 5 minutes. (3-5 minutes is about the ideal length for a single version of a song.) In perhaps the most dramatic example of editing for time, the album version of "In-A-Gadda-Da-Vida" by Iron Butterfly is just over 17 minutes in length; the radio edit of this song is just under 3 minutes.
Another reason for doing a radio edit of a song would be to omit objectionable language, such as the famous "Seven Dirty Words," which would otherwise result in punitive action by the FCC or other authorities. For example, Nine Inch Nails' "Closer" contains, in its chorus, the line "I wanna fuck you like an animal"; in radio edits, the word "fuck" is omitted. (There are actually two different radio edits for "You Oughta Know" by Alanis Morissette; the usual radio edit blocks only the obvious part of the line "And are you thinking of me when you fuck her," but MTV used an edit that also blocked part of the line "Would she go down on you in a theater".)
Radio edits usually sound almost the same as the song as it exists on an album, except for the time and language cuts, but can sometimes sound very different. In the case of "The Mummers' Dance" by Loreena McKennitt; the album version is done in a gentle Irish folk music style, but the radio edit (and single version) is a remix by the British group DNA, and has an electronic dance pop feel to it.