In Apple's iTunes, a Genius playlist is a special automatically generated playlist based on a specific music selection. By choosing a song and creating a Genius playlist, iTunes will create a playlist of related songs from the available music in your library.
In this way, you can create a playlist of similar music simply by selecting a song, instead of having to peruse your library and manually create a playlist.
In past versions of iTunes, you could create Genius playlists by right-clicking the song and choosing the option to create a Genius playlist based off it. In the latest version, Apple has a quick way to create a Genius playlist from the current song being played.
While a song is playing in iTunes, simply hold the Option key, and you will see the Previous control button turn into a revolving arrow button for the creation of the Genius playlist. Simply click this button, and the current song will be used as the basis for the Genius playlist, as opposed to any selected song in your library. The playlist will then appear in the "Up Next" menu in the song information window.
After the Genius playlist has been created, the playlist button will remain, so you can continue to click it and create a new playlist off the current song, should you wish to do so.