Fox's shine is what makes him fox. You can drill shine and then wavedash to grab or just keep waveshining them off the edge if they suck. If your opponent shields a lot of the time if you L cancel you get them with the shine. If they are too close to you, shine. If they are trying to recover and get back on the ledge/stage, jump off and shine them. This is called a shine spike, and it's incredibly cool to see.
If you want to know about falco's shine, it is also very important. You can shine them, and it will knock them up allowing you to jump up and use your Down Air attack to hit them down, and then fast fall and shine them again before they get back up, knocking them back into the air where you can continue the combo or Back Air or Forward Air them. Falco's shine sets up huge combos, and if your good at them you can pull them off on even the best of players. For example, PC Chris gets ken pretty badly with falco's shine combos, although Ken usually breaks out of it before it gets too serious.
Also, I tried to not use any smash terms because if you didn't know what a drill shine is, i dont think you would know any smash terms. Actually, not that I think of it, i dont even know why i spent my time writing this reply. I hate fox and falco. I should just delete this all. w/e, i already wrote it anyways.