It is the solidification process where the liquid steel is poured into a bottomless mold with the shape of the cross-section of the semi-finished product to be manufactured.
It is called continuous because the liquid steel never stops in the mold, so that you get continuous as-cast products without stopping the line.
The main advantages of continuous casting are the high productivity over conventional castings and the direct obtaining of primary products (slab, bloom and billet) which does not have to be reheated to be treated in a roughing train.