An Embassy is a group of people on a diplomatic mission. The head of the Embassy is an Ambassador and this person and those who work for them enjoy what is known as diplomatic immunity. This makes them immune from the laws of the host country (the country the diplomatic mission is to).
The building that they work in is also usually known as an Embassy and it is protected by treaties that mean that no one from the host country can enter its grounds without permission. However, contrary to popular belief the grounds of the Embassy are not considered the sovereign territory of the diplomatic mission using it. This protection is also extended to any residence members of the diplomatic mission live in while on their diplomatic mission.
The purpose of a diplomatic mission is to for them to represent the state that has sent them. They meet with members of government, business leaders, etc, etc, etc. They work out the details of treaties, maintain good (or even bad) relations, at times they may even be informed, or inform, that a state of war exists between the two nations.
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