Like most Frost spells, it can be used to set off Frost Runes from a safe distance (though Ice Spike or Ice Storm may be preferable due to their greater range).
Frostbite is the only Novice level Destruction spell (barring Arniel's Convection, which is learned as part of a quest, and Vampiric Drain, which is gained through vampirism) to not be known at the beginning of character creation. All races start with Flames, while Dunmer start with both Flames and Sparks, but no races start out with Frostbite.