Supply Cases are used by military personnel to transport weapons and gear for operations across the globe. They can contain any number of items – weapons, body armor, support equipment, etc. With all the operations carried out through Central Command, quite a number of these have been mistagged, mislabeled, and mishandled to the point that we don't know what they hold or which operation they were intended for.
(Different Supply Cases contain different gear items )
Central Command has authorized the Depot to make these surplus Supply Cases available for purchase to mercs that are sufficiently ranked. Once you've reached the rank of Corporal, you'll be able to buy Supply Cases with Gear Points (GP) through the in-game Shop.
(Buying a Supply Case from Shop/Storage)
Supply Cases may contain non-standard issue weapons or gear items – exclusive items such as the L96A1 Ghillie sniper rifle and the M590 CQB combat shotgun – that can't be bought directly from the Shop. Usage time for the item you receive is also up to chance, so if you're lucky, you may receive 90-Day usage rather a 1-Day use for your gear item!
"Be warned: We don't know what's exactly in the cases, so you won't know what you've bought until you buy it... and the Shop doesn't accept returns on open cases. No refunds, and we ain't sorry about that.So if you trust your luck, soldier, buy a Supply Case and hope for the best. You may be pleasantly rewarded... "
(Opening a Supply Case and Receiving Your Item)

Supply Cases can be bought at the 'Other' tab of the Shop/Storage screen, and are bought with GP like any other weapon or gear item. Click on the specific case you want, confirm your choice, and the case will automatically be opened, showing you the item you've acquired.
If you receive an item from a Supply Case that you already have, you will receive additional usage time for that item instead, rather than a separate duplicate weapon.