Sorry, this is probably a really silly question, but I''ve seen the term used, and I even have a ring that was described as having an airline, and I don''t know what it refers to!
Although if you plan on putting a diamond with a diamond halo, and want the overall look of your diamond to look Bigger then you might want to get a no airline halo so when you look from a distance you perceive the center to look larger than it is. However, if you wanted to accentuate the setting a bit or the center stone, then I love the look of noticeable airline if that makes sense?