What is a draft beer? What constitutes a draft beer, and how different is it? I see this term plastered on beer cans, but I have no idea what it means, or how it affects the beer's taste.
Draft beer is another name for Draught beer, it means that the beer is served from a cask or a keg.

When you see this term plastered on beer cans, then it means that it's a Canned Draught.   The can contains a widget. This widget was invented by Guinness in order to let consumers drink a Draught beer at home. This differs from a typical can in that the beer is usually carbonated by forcing CO2 directly into the bottle/can or intermediary vessel, or by "bottle conditioning" (leaving live yeast in the beer and adding something for it to eat, creating CO2 and more alcohol).

Everyone on this site should be thankful for Guinness for having invented the widget!