Foreign deposits are taken in by international branch locations of US-based banking institutions. Banks are not obligated to pay FDIC premiums on these deposits.
Foreign deposits are placed by customers into a US-based bank branch which is located in international locations. Because it is outside of Federal jurisdiction, banks are not subject to the same capital reserve requirements and do not have to pay FDIC insurance on the deposits.
This can be advantageous for a bank, obviously. It can also be convenient for Americans traveling abroad to be able to deal with a US-based bank for their banking needs while overseas. Military banking institutions overseen by the Department of Defense are still FDIC insured.
The fact that other foreign branches are not FDIC insured should be a warning signal to customers, since their deposits may become entangled with risky offshore ventures, but a 1990 publication reported that 51% of all deposits owned by US banks were held overseas. At that juncture, the FDIC was campaigning to ensure all foreign branch deposits, probably because this would have allowed them to receive premiums for these deposits from the banks.
This proposal came in the wake of the savings and loan crisis that had bankrupted the FSLIC, which insured savings and loan deposits, so the FDIC foreign branch proposal did not get very far. There is simply too much unknown risk in international locations. In 2013 the FDIC finally gave definite statements that it does not insure foreign deposits.
Once deposits are in a bank, they represent a liability on the balance sheet, because the bank has use of most of the funds in the meantime, but they must be paid back to the depositor. FDIC insurance guarantees that this liability is repaid, up to a limit of $250,000 per person and banks pay premiums domestically to transfer this risk to the FDIC.