The development of the mature form of feudalism, the Monarchy, turns the center of imperial power into a shining jewel of civilized life. A single ruler, a splendid king or queen now concentrates all the attention and admiration of his or her subjects, centralizing most entertainment, culture and even commerce.
This level 3 Policy is a great all-around bonus, giving an immediate boost, as well as subsequent bonuses as the Population of your Capital increases (as it should, thanks to the other Policies in the tree). The only consideration to make is whether you should adopt it before or after Landed Elite. Because the latter has a truly outstanding long-term bonus, it is usually better to adopt it first; if you're strapped for cash, however, or in trouble with your Happiness, Monarchy will greatly help you. Again, the more citizens in your Capital, the greater the immediate effect!
As it affects happiness and therefore expansion potential, it is one of the longer lasting policies from the two early policy trees. It contrasts with Meritocracy from the Tradition tree, which is proportional to the population as a whole (instead of just the capital).
Monarchy is a form of government where power is vested in an individual. Often, but not always, power passes to the monarch's heir upon the current ruler's death. (There are some elected monarchies, but not many.) Monarchy is similar to despotism, but with one important difference: the monarch rules within the state's laws, while a despot is above all law. It is of course quite possible for a monarch to be a despot - but it is also possible for a monarch to be part of a political process which allows the people a good deal of freedom. Great Britain would be an example of the latter.