The Band is a magical ancient artifact that, if the proper owner possesses it, can unlock the secrets of the monsters' lands and the owner's true inner potential. It is an reddish orange band that resembles a thick bracelet, but gives the owner many abilities. Ellie is the current owner of the Band, though Priscilla wants to steal it for her own.
It can activate the Ancient Rune Statues, giving Ellie new abilities and attacks, and there are times in the game where Ellie says the Band is calling her to new places in the monster world. The Band is used for multiple blaster attacks throughout the game, and can be upgraded by Jinx. It's the first thing the player learns how to use, besides basic motions like walking.
Ellie uses and wears the Band throughout the game, and it is unknown whether or not she takes it with her when she returns home. She is not seen wearing it in the Ending picture of her, even though her wrist is in plain sight. This could mean she left it behind, or that she simply wasn't wearing it. Neither possibility is implied.