These briefcases are used specifically by the Four Horsemen of the Apocalypse, particularly by Death and Famine, for transporting souls.
Overview
Season 5
Demons collect souls for Famine using this. One of these demons are intercepted by Sam Winchester, and he brought it back to the motel. There, Sam and Dean discover a soul was encased inside. They later use this information as a means of tracking down Famine.[1]
Season 6
Death carries in Sam's soul from Hell using the briefcase. As Sam begs him not to put the soul back, Death opens his bag and Sam's soul shines brightly. Death soon inserts Sam's soul back into his body.[2]