Here is a typical working flow chart demonstrating how the transit warehouse works. After registering on a transit warehose website, you'll get an address in the country where you buy your goods. Then, you set up this address in your account of Taobao, Amazon or other platforms so that the merchants there can send the goods you order to that address. As soon as the transit warehouse receives your goods, they will handle your goods in the process shown in the flow chart and have it transport to your place promptly.
As the transit warehouse will pack a huge amount of the goods in batches for transportation, the cost you share will be significantly lower than that incurred should you ask the merchant to send the goods to your place separately.