A daimyō (大名, daimyō, English TV: Feudal Lord, Literally meaning: Great Name) is the political leader of a country. A daimyō is responsible for all decisions concerning their country, from alliances to the annual budget to the privileges allowed to the country's hidden village. Daimyō are therefore one of the single most important individuals in the entire country and hold the highest degree of political power, such that they are given special protection by the Allied Shinobi Forces during the Fourth Shinobi World War.
The final decision in the appointing of a new Kage for their nation's respective hidden village can rest within the daimyō's authority. In the case of Konohagakure, the Hokage typically selects their successor but if the Hokage dies or is otherwise incapacitated, this responsibility moves to the daimyō. The daimyō is advised by his committee, the Konoha Council, the Jōnin Commander and a representative of the Anbu during this selection. Once a candidate has been selected, the incumbent must then be agreeable to all the jōnin before they are sworn into office. For example, Danzō Shimura was selected as the Sixth Hokage Candidate when Tsunade was in a coma but died before the jōnin could convene and thus his position was never made official.
Daimyō frequently attend the final round matches of the Chūnin Exams, either to bet on the fights or to seek out up-and-coming talent. In Shikamaru Hiden, daimyō are noted to always reside in their country's capital city, constantly waited upon by numerous attendants and advisers who, themselves, tend to be overbearing and arrogant to the general population. Gengo blames daimyō for the world's many conflicts, as daimyō tend to squabble between themselves that they then send shinobi to sort out. Because the daimyō don't personally involve themselves in these wars, they never truly appreciate the horrors of battle and thus inevitably get into some other petty conflict at some future date.
The political importance of a daimyō is such that assassinating one of them is considered a crime, as Kisame Hoshigaki was condemned as a missing-nin as one of his crimes involved in killing a daimyō from another country.