If more people adhered to this principle, the world would be a better place.
The principle is this: when someone presents an argument, interpret inasmuch as possible every point in a fashion that would be most beneficial to that argument. In other words, the maxim of innocent until proven guilty applied to human discourse.
The principle of charity goes beyond granting someone the benefit of the doubt because it implies making a conscious effort to make someone else's argument stand on its own two feet. Whereas giving someone the benefit of the doubt is a passive activity (all things being equal and unable to decide either way on the state of an argument, assume it is correct), the principle of charity turns this passivity into something more active. The idea is to remove some of the strain from the person who presents an argument to the person hearing the argument.
There are several reasons why it is a good rule to follow broadly. First, because it makes it more difficult to fall into the trap of fallacies such as ad hominem or straw man. Second, because by keeping this as a general principle forces one to actually listen to what the argument says and therefore makes one work harder in order to support or debunk that argument as desired (therefore, more likely to be correct when supporting or debunking).
The principle of charity also makes life simpler. Say you're reading a book that you know contains an error or omission that significantly alters the meaning of what is being said. If you recognised it as an error, then just take out a little pencil and make an inconspicuous correction in the margin for your own use (or quietly /msg the perpetrator of the error, as the case may be). Do not make a big fuss, or conclude that the entire argument is faulty because of a small imperfection. Be kind to the person who fell into an error. The case of an error of omission is more delicate, but you should also generally assume that whoever was writing either made a deliberate omission because it did not seem important to mention that point, or will address it later on as needed. This avoids unncessary petty arguments.
No one is recommending pussyfooting here. If you need to argue and express contrary opinions, please do so, and we will defend to the death your right to do so. Just before you argue, grant your opponents as much as you can, and arm them with every defense and attack that you can. Now you may argue. Good luck.
By the way, the principle of charity is sometimes known as "politeness" or "fair play", especially when applied to contexts besides arguments. Walk in someone else's shoes for a mile before you judge them. It also makes life simpler in those instances.