“rel” is a player parameter, as specified here:
https://developers.google.com/youtube/player_parameters#rel
To add player parameters to iframe players, you need to specify the playerVars property of the second constructor argument (at the time of writing this is documented here, and on the IFrame API documentation page)
e.g.
new YT.Player('playerid', {
height: '550',
width: '840',
videoID: 'video_id',
playerVars: {rel: 0, showinfo: 0, ecver: 2}
});