Fly is a condition that allows you to move without touching the ground, and with more control than levitation. A flying player can ignore water, lava, and most traps, gains a bonus to stealth and carrying capacity, receives twice the normal benefit of the Swiftness spell, and gets a small increase to speed if the character is a tengu carrying <70% of their unburdened carrying capacity.
Flying also reduces (self) Static Discharge damage and completely stops weapons of electrocution.
Its only downside is that you take extra damage from Airstrike.
In 0.13 flight will not protect from any kind of electric damage.