Anything of monetary value — dinner, lunch, a box of candy, tickets to a fundraiser, a pen, artwork, a reception, jewelry, etc. A gift is also something that's not quite so concrete — such as a discount, invitation to an event, entertainment, or forbearance of a loan. A gift also includes services such as free tax preparation.
Something given, a present, the act of giving, the power or right of giving. Corruption occurs when the gift is meant to, or would possibly influence, the public official.