If something's done officially, it's done formally, often with the backing of some kind of authority, like a government. You might be elected president in November, but you won't officially take office until January of the following year.
The adverb officially can describe something that's done publicly in an official and formal way. A company's CEO may officially resign after speculation about money laundering became public. An advertising campaign might officially launch with a Super Bowl ad. Officially can also describe something authorized by a government or other organization with authority. The government may officially announce that unemployment has decreased in the last six months.