Avia
Line Flying is day to day flying in an airline.
Line Training is training "on the line."
Once you've done your type rating you are trained to fly the aircraft but all you will of only ever done is a few circuits, so the next stage is to train you how to operate it on the line with passengers. Typically this will be around 50 sectors with a training captain.
Take a look at this thread.
http://www.pprune.org/forums/showthr...=line+training
SW