The advent of something means that it's finally here. You might be waiting for the advent of a new iPhone or for the advent of cloning. Don't hold your breath.
Generally, the noun advent is used for the introduction of something important. The twentieth century saw the advent of many important inventions — including television, computers, and microwave dinners. If the word is capitalized, it has a religious meaning, referring to the period, observed in certain Christian religions, that begins on the fourth Sunday before Christmas (December 25).