The system is based on feudal where vassals hold inherited lands and provide military services, homage to the lords. However, the system also resembles the bureaucratic and modern politics as well, an aspect that is not seen in the European feudalism.
Unlike feudal systems found in the medieval history of Europe, in the system, the two level of governments exist, the shogunate in Edo and provincial domains throughout Japan coexist; the domains are given certain sovereignty and are allowed an independent administration in the fief in exchange of loyalty towards the Shogun while the shogunate is responsible for foreign relationships and the nation security. The shogunate and domains are both daimyo, translated as feudal lords with its own bureaucracy, policies and territory. The shogunate is the foremost, strongest and largest among them, thus, it is primarily responsible for its territory, the fief of the Tokugawa house just like other domains. Tax are collected and economy was conducted in terms of each domain. Besides the duty as the daimyo, the shogunate is also concerted with controlling the social classes, maintaining the order if the disorder is beyond the power of the domain and making policies across Japan.
Despite the system, the emperor in Kyoto is still a legitimate ruler of Japan. The administration (taisei) of Japan is the task given from the Imperial Court in Kyoto to the Tokugawa family, which is returned to the court in the Meiji restoration.
The foreign affairs and trade was monopolized by the shogunate--the trade yielded a huge profit to the shogunate. Foreign trades are also permitted to Satuma domain and Tsushima domain.
The shogunate has a power to discard, split and transform domains--those are essential tools to control domains. The Sankin-kotai or the alternative residence in Edo required domains to have hostages such as heirs and wives resident in Edo and visit the Edo each alternative year, which imposed a huge expenditure to the domains.
Reference
http://hkuhist2.hku.hk/nakasendo/tokupols.htm