Dropshipping is a way to order from a vendor without having inventory on hand or in a warehouse.
When a customer places an order with your company, you then order from the vendor and have it sent to you and you send it to your customer under your brand or the vendor will send it out under your brand name.
When having an out of country vendor they are not able to ship under your name due to customs regulations, but they will offer dropshipping services.
Some companies will send the products to your customers directly from their factory or warehouse. You can send your promotional products and they will add it to your package for a small fee and ship it to your customers.