"Line breeding" means choosing geckos that possess the visual characteristics you like and breeding them together to hopefully produce an even better looking specimen. I think it's called "line breeding" because usually this involves breeding from the same "line" of geckos, ie. breeding gecko that are related to each other. This is acceptable for a few generations. Usually people who do this kind of breeding will, after a few generations, breed to a gecko that's not related in order to maintain genetic diversity. This is called "outcrossing' and kind of goes hand in hand with "line breeding" to produce geckos that are the best representations of the characteristics you like but also genetically diverse enough to produce future generations of healthy offspring.
Make sense?
Aliza