The term playlist can be used in a few different ways. First, a playlist is a list of songs that a radio station plans to play on a regular basis. The same term is used by MTV, VH1 and other music television channels for videos they play regularly. Radio stations that work with playlists usually have a tiered listing system - songs that are on the A list get played X number of times a day, the B list slightly fewer times, and the C list fewer again. In most cases, DJs are bound by the playlist and obligated to meet the requirements of the list before they can select music themselves to play - in fact, many radio shows are determined entirely by the playlist or the DJ may get as a few as one or two "free plays" that they can use to play songs they think are great. If you hear that a song is in "heavy rotation," it means that it is high on the playlist.
These kinds of playlists are typically determined in playlist meetings, during which radio pluggers meet with reps from the radio station, play the songs they are promoting and try to convince the station to put the songs into rotation. Radio is controversial these days because a lot of playlist decisions are seemingly made based on the budget of the record label, and the Sony BMG payola case is one of many recent examples of how big budgets can sway playlists.
Playlist can also mean a list of songs played by a DJ during their show. This includes songs on the official station playlist and songs the DJ selects. If you hire a radio PR company, if they get a station to play your song, they will send you a copy of the playlist that features the song. Note that just because you are on the playlist for a show for a certain day, it does not mean that you are on the official station playlist and that your song will be in rotation to played on a regular basis.