A line pretty much is just something to describe where they come from EG: my Silver duckwing old english game bantams came from the Herman woody line (indirectly though).. Which is the most best known line basically (Not saying it is the best, but one of).
However, many people who say "This descended from this line" use it as a "It's good quality" but buyers need to look into that, just because it has the name attached and it came from that line doesn't mean it will be good... Once it leaves the breeders hands, and is in yours. The offspring are then your line because you bred/selected them...
You could start with a hatchery too, doesn't necessarily have to be a breeder. A line is a line, regardless of show quality or pet quality..