Draught beer or draft beer is beer that is served via pressurized line or hand pump/beer engine from a holding tank, barrel, keg, or cask to the glass as opposed to being poured from a bottle or can.
Beer conditioning typically occurs after primary fermentation has completed, and the beer has been racked off the yeast and trub bed to a different vessel such as a secondary fermenter, barrel, keg, holding tank, cask, or bottle. The beer then conditions over time; the length of time typically depends on the style of beer, and the type of conditioning that is desired.
If you are brewing an American wheat or perhaps a dry hopped pale ale, where a very fresh taste or aroma may be desired, then you would want a minimal conditioning time. But if you are brewing a barrel aged stout or a Flanders red sour, you may need to allow the beer to condition for over a year depending on the conditioning environment and desired flavors.
A beer engine is a traditional hand-powered pump that is used to transfer beer from a cask to a serving spout.
Cask conditioned beer refers to unfiltered and unpasteurized beer that has been conditioned in and served from a cask. This method will impart a distinctive flavor. Cask conditioned beer is naturally fermented and is typically served from the cask using a beer engine or hand-powered style pump as opposed to pushed using a CO2 tank. Cask beers tend to be served with lower levels of dissolved CO2 than one might find in a typical kegged beer. The shelf life of a casked beer is also much shorter, and the potential for oxidization is much higher since the cask walls are air permeable.