Flares are miscellaneous equipment automatically provided to all your Soldiers when they embark on a night mission. They weigh nothing, are infinite in quantity, and occupy a space in the Quick Grenade Slot menu.
Night time combat limits the line of sight of soldiers from 18 tiles to 9 tiles. This makes night combat significantly more difficult. As such flares are used to attempt to combat this disadvantage. Throwing a flare requires a relatively modest 20% of a soldier's TUs. The flare will light up upon hitting the ground, providing a small lit area not dependent on your soldiers' tactical lights.
Note that you cannot pick up a lit flare.