A moulded bra is a bra where the cup is made out of a single piece of fabric and has no seams through the middle of the cup. (As opposed to a bra with the cups made of different pieces of fabric sewn together to form the cup shape).
Moulded bras may or may not also have foam padding in the cups.
A moulded bra cup holds it's shape, even when not being worn. If you set it on a table, the cups will retain their dome shape.
Moulded bras get their name from the heat moulding process that makes the cups. The view below illustrates this clearly, staring at 2:20s in the video, you can clearly see the second bra made from lace, is a moulded bra that is not padded.
Benefits of Moulded bras:
Moulded bras provide a rounded shape to the bust (great for sagging busts by creating a perky look)
Moulded bras reduce irritation on the bust or nipples due to the absence of seams
Moulded bras won't show seams through t-shirts and tops
Moulded bras with foam cup construction will eliminate nipple show through
Types of Moulded bras
Foam cup bras (also sometimes called contour, padded bras or T-Shirt bras)