An official recognition of a person in the character of consul or commercial agent, authorising him to exercise his power. The word is Latin, and means, “he may exercise” [the function to which he has been appointed].
“The Northern Patriotic League (Oporto) has decided to petition the Government to withdraw the Exequatur from the British Consul here.” —Reuter's Telegram, Tuesday, Feb. 11th, 1890.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Exequatur from Infoplease: