When you publicize something, you let the whole world know about it. The president might hold a press conference to publicize a new policy, or you might use Facebook to publicize your new relationship status.
To make something very widely known, or to make an official announcement about it, is to publicize it. Companies publicize new products and sale prices, and politicians publicize the missteps and bad policies of their opponents. The verb publicize was first used at the beginning of the twentieth century, combining public, with its Latin root of publicus, "of the people, common, or general," and the verb-making suffix ize.