Devices are items exclusive to Pokémon Mystery Dungeon: Gates to Infinity. They are elemental consumable items that raise the stats of Pokémon of that Device's type.
They are items that are consumed, so they disappear after use, if GTI is anything similar to EoS.
Edit: I did more searching, and found that the stat boosts from Devices are actually pernament, according to this thread. I usually don't use random threads as sources, as they are unreliable, but I has a look at the descriptions for other pernament-effect items too, and found that they are described the same as Devices. So if you use a device on the correct type of Pokémon, it will permanently raise your Attack, Defense, Special Attack and Special Defense by two stat points each.
Sorry for the confusion.