A standard-issue pre-War flare, designed for signalling and temporary illumination. Though the paper packaging tends to be a little worn centuries after the War, they reliably lit up when one twists the cap.
An activated flare is useful for reducing the ambient darkness, making finding items on the ground easier. Hitting a target or approaching them with the flare active will also illuminate them, eliminating the high penalties for firing in darkness. In the rare situations where the player can approach enemies without causing them to go hostile, this allows for waiting until nightfall, then dropping lit flares next to the targets or spreading them around the battlefield, to eliminate penalties for shooting in darkness for the player character, but keeping them for enemies.
Another use is as a cheap Throwing weapon. A well aimed hit to the eyes allows for blinding enemies (even if they wear power armor) or killing them instantaneously with Better Criticals. Cheap and lightweight, the flares can be quite the weapon. Finally, since they cost $35 apiece, they're a decent source of revenue early on.
Vault 13: Three flares are the vault starting equipment for the player.
Vault 15: Inside the emergency gear locker in the airlock.