The immediate effect of the American Revolution was that the American colonies became a free and independent country.  This revolution did not bring about any other huge and immediate changes.  This is why many historians argue that it was not a real revolution at all.

After the end of the Revolutionary War, the British left the colonies (for the most part) and ceded control to the new American government.  Americans ruled themselves instead of being ruled from afar.  The new nation was set up under the Articles of Confederation.  The new nation was a loose confederation of states, not the centralized system we now have.

Outside of this, there was little change.  The same people who had been important before the war were, for the most part, important after it.  There was no change in the status of women.  There was no change in the status of non-white people.  The system of government did not change radically.  Therefore, this was not a revolution with immediate effect.  There are those who say that the Revolution caused a long-term shift towards more egalitarianism and democracy, but that shift would not become clearly apparent for decades.  The only real immediate effect was the independence of the former colonies.