First things first: is it molded or moulded? If you're British, it is moulded. If you're from the U.S. then it is molded. Just like colour = color! Moving on.
Molded bras are exactly like soft-cup bras, except the main difference is the synthetic, molded cups. These molds are formed using heat on machines and they are one of greatest luxuries mankind has ever known (just my opinion, but oh well). Each layer of the bra/cups is then heat set to each other (which is why they don't easily pull apart). There's a silent Youtube video below if you want to see some being made, small scale.
Because cups are designed on a computer before manufacturing begins, the shape of the cup can vary greatly between manufacturers. The video above features a rounded shape but you could also achieve cone shapes or flatter shapes, as well. Bras are slowly becoming more and more heavily engineered (which increases cost, as does raw material increases, too). The video below is a short animation of how a bra cup is created.
One of the clear benefits to a molded cup, though, is that the outer and inner fabric is applied via heat instead of being sewn together, panel by panel. This removes some of the hands-on, human intense process of sewing individual panels. That being said, bra manufacturing is incredibly complex, starting from the design all the way to the finished product. If you want a brief introduction to this aspect, don't be afraid to watch the video below from CCTV.
What are the downsides to owning a molded bra? Storing and traveling with these bras can be a challenge, especially because you shouldn't turn these cups inside-out. The best method for storing them is "nested" so that the cups sit within the cups of the bra in front of it. A close example is below by Elle's Blonde World.
Another downside is they absorb sweat! This means that they can stain easily and might have to be washed more often than soft-cup bras. If possible, do NOT machine wash your bras and especially not molded bras. Leaving them for a soak is OK in a gentle detergent and I have even Oxyclean-ed mine because honestly... ain't nobody got time for that! BUT if you want your bras to last, I suggest you buy a gentle detergent like the Nordstrom Lingerie Wash.
Remember, because molded bras are made from synthetic material (the spongey portion) then they can't really be re-used. So if you are Eco-conscious, then consider purchasing only natural fiber bras or just soft-cupped bras that take up less space.