Anything mayoral has to do with the official leader of a city or town, or with the office itself. In a mayoral election, candidates are vying to become the highest-ranking city official.
Mayoral is from mayor, which derives from the Old French maire, "head of a city or town government," and a Latin root meaning "great." This adjective is used to talk about things related to the mayor, from the mayoral residence and mayoral duties to mayoral election campaigns and speeches. If you have mayoral ambitions, that means you dream of heading up your town's government one day. The word mayoral can also be used as a noun when referring to any overseer or foreman, especially of a ranch or an estate in Spain or Mexico in the 1800s.