All payment systems have this setting, but typically it is most
commonly used with the 'PO - Offline payment' system. If checked, only
users who have pre-approved will see this option at checkout and hence
be able to use it. This way, you can accept orders for payment later
by customers who you have granted credit terms to, but new customers
and others that are unapproved must make payment by credit card or
another online payment system.
We would advise that even if not using the PO option on your
store, you keep it set to ON but then set it as
AuthorizedOnly, which will prevent the public
from using it unless you specifically allow them to. This is because
orders of zero value (which can occur either if some items are free,
or if a coupon is used for the full value of the order) will use the
PO checkout route. If you turn the PO option off, you will
effectively prevent the store bypassing the payment system for zero
value orders.