So called, (as far as I can ascertain) after a Belgian distance caster in the 1930's called Albert Godart. This particular cast can be used in a variety of different ways, but the two most useful uses I have encountered when fishing myself are:
(a) when casting heavy or bulky flies on shorter leaders.
(b) when casting a team of light flies on longer leaders.
Heavy / Bulky Flies
As this is a very rounded and continuously moving cast, when fishing with heavy / Bulky flies it enables you to keep the fly away from you (safe) and under tension at all times until it is actually delivered. It also prevents heavy flies from kicking down behind as they would do in a conventional overhead cast. This is because the back cast (in a Belgian cast) accelerates from below and is therefore climbing upward as it is being drawn forward again into the forward delivery. Many saltwater casters will also use this cast when delivering very large lures, often in conjunction with a double haul.
Although this cast enables you to open up your loops on both the back cast and the forward cast a tight loop is achievable on the forward cast where required which you may wish to do when using a single heavy or bulky fly.
Team of Flies
When fishing with a team of flies on a very long leader, casting tight loops will do you know favours whatsoever, as it will only result in numerous tangles and therefore wasting valuable fishing time, so imagine the advantage of being able to open up your loop to prevent tangles and still achieve a relatively efficient cast.