Light Shield is one of the Mystical abilities. You need 12 Mystical use points to be able to cast it. If you have 11 use points plus your bonus 1 pt for being a Mystical user, you can still cast LS even though it won't show up on your M menu. This is true for every M ability that costs multiple points.
Light Shield's purpose is to cut the damage you receive in half. As soon as you cast it, it begins to work, and continues working for the remainder of the fight. Even if you get revived by a fairy in the middle of the fight, the light shield still remains. If you try to cast a second LS on top of the first, it will let you spend the points, but it won't actually cut the damage you receive any further.
It can be used on the dragon, on forest monsters (though it's never really used there), and on offline player fights regardless of what level you or your opponent are.
Strategic use Edit
LS is a huge advantage against the dragon, since it has so many HP and can take many strikes to kill. Players who start M have it for every dragon. Players who start T aim to have it for the second dragon.
LS is also a handy advantage during offline player fights. Usually, attacking another player on your level--who also has similar equipment--brings 50/50 odds at best, but with LS you can attack them with a pretty good chance of winning. It's also useful for helping you survive the strikes of a higher-level player who either has much better equipment, or who is more than one level above you.
Shatter + T is a stronger attack than LS + 2T, but sometimes you're not sure if you'll be able to survive two hits from your target without LS. It's a judgment call at that point. LS is the defensive route, and Shatter is the offensive route.