A foreign embassy is the official office of one country in another. It is usually in the capital city of the other country. It is where the ambassador and other representatives of the home country work. Much of the diplomacy (talk) between the two governments happens there. They represent their country to the host government. The embassy represents the interests of the entire country and is fully responsible for the relationship between the two countries.
The head of the embassy is usually an ambassador, but can also be a minister, high commissioner, or other level of diplomatic personnel appointed by the sending country to represent it.