Weapons and gadgets can be bought at the Weapon Shop, with the exception of event boss drops.
Weapons enhance your basic attack damage by multiplying it. For example, a normal punch of 100 damage, multiplied by a normal dagger, would be 130 damage, instead of 100. Not all weapons have the same rate of attack, as the dagger does more damage per hit then the katana but the katana does more damage per second via spamming
Gadgets in the game are armors/accessories from the anime/manga Boku No Hero Academia which enhances your quirk. Currently, the only gadgets you can buy are Gauntlets, Shadow Cape and Iron Soles (Iron Soles can be upgraded to further enhance the features).
Loot comes in 2 forms, common and rare. Common loot has a 5% chance of dropping while rare loot has a 0.025% chance of dropping.
Boost is basically the damage multiplier you get flat out before quirk multipliers for attacks even come into play.