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An embassy is the office of the ambassador, who represents a foreign country to a host country with formal soverighty recognition.
A consulate is like a junior emabssy, and is the office of the consul (or consulate-general), who is a diplomat appointed by a foreign country to foster trade and take care of its citizens abroad, as well as minor diplomatic tasks such as issuing visas.
In a host country, there is only one embassy from another country, and is usually located in the capital city. Whereas there can be more than one consulates from one country, especailly big ones like the United States, which, for example, has consulates in major cities in China, as well as Hong Kong.
An embassy takes care of the same administrative duties as consulates, but it also represent its government abroad and handles all major diplomatic issues. Since its presence means official recognition of sovereignty, the United States can not have an embassy in Taiwan, only a consulate.