Being broody is when a hen wants to sit on eggs and hatch out chicks. During her setting she will stop laying eggs.
I think that the High Medium and Low production targets what the 'average' hen will lay -- such as 250 eggs per year. If the hen exceeds that she will be considered a high producer and if her egg total is below that average she would be considered lower. Some breeds are raised specifically for egg production --especially crossed breeds (hybrids) such as Golden Comets, Black Sex-links, Red Stars and Production Reds. There are numerous names for the various hybrids too so that adds a layer of confusion. Some breeds are raised for their visual appeal or feathering, and the raisers don't concern themselves about egg production.