The Revolutionary War was very revolutionary for its time because during the 18th century it was almost unheard of to go against the monarchy. The movement of our patriots to stand against the monarchy for independence coincided with the Age of Enlightenment or the Age of Reason. The Age of Enlightenment began in the 1650's and ended in the 1780's. This was a time when thought shifted from traditional lines of authority; such as believable information only coming from a monarch; to individual reason, analysis and thought. Many nations were watching the American Revolution to see if such a movement would be possible in their own country. The English army at that time was the strongest in the world and no one dared to go against them. When the United States won the war other countries, such as France, took notice of the outcome and thus launched their own independence movements. Without the American Revolutionary War the French peasants would have never risen against their own monarchy. It is the spirit of the American Revolutionary War that continues to inspire others.
This is a very typical question to ask in US history classes, in part because you can argue it in many different ways. Let us look at three possible positions on this topic.
First, it is possible to say that the American Revolution was not very revolutionary at all. We can say that relatively wealthy white men ran the colonies and relatively wealthy white men ran the United States after it became independent. This was not a revolution that overturned the social order. It did not bring rights for women or non-whites. It did not redistribute income or power to the poor. It generally just took a colonial elite and put them in power without having a British elite above them as there previously had been.
Second, it is possible to argue that the American Revolution was revolutionary. The United States, even dominated by white men who were relatively wealthy, was much more democratic than the UK was. The US explicitly protected things like civil liberties while the UK did not have explicit protections for freedom of speech and actually did have an established religion. In these ways, you can say that a major break occurred with the Revolution.
Finally, you can take the approach of Gordon Wood in his influential book The Radicalism of the American Revolution. Wood argues that the Revolution was not very revolutionary in the short term. However, in the long term it was extremely revolutionary because it encouraged people to think in radically new ways. White men of all economic statuses came to think of themselves as equals. This egalitarianism has spread over time to the point where women and non-whites can now generally see themselves as equal to white men. This, Wood would say, is the true reason why the Revolution was revolutionary.
Any of these arguments is plausible. Which one makes the most sense to you?