The fall of the Berlin Wall. It symbolized the end of the old division between East and West Germany (out with the old). After that, Germany was reunified, bringing in new economic and social systems (in with the new). This was a huge change not just for Germany but also for the whole of Europe as it signified the end of the Cold War divide in that part of the world.
The French Revolution. The old monarchy system was overthrown (out with the old) and a new, more democratic system was attempted to be established (in with the new). There was a shift from the rule of the king and the aristocracy to the ideals of liberty, equality, and fraternity for the common people.
The Industrial Revolution is a good example. Old, manual - labor - based production was replaced with machine - based manufacturing.