First and foremost we will finally know that we are not alone in the universe. That has been one of humankind's oldest and most profound questions. We will have learned that life is possible elsewhere, that we are not the center of everything, and that we're not so damned important as some of us think.
We will be forced (and fortunate) to see ourselves as sharing this universe with other beings, who may have knowledge we could use. For one thing, we might (if we could skirt the language and distance barriers) find out if they had something equivalent to a nuclear age, or to terrorism or famine or disease or hatred or irrationality, or even political resistance to societal advancement... and how, if so, they dealt with these challenges. I personally would ask them if they had to deal with lack of compassion and of critical thinking, two of the personality traits which so endanger human beings in so many ways.
But as Ken E wisely touched on, there will be people who refuse to believe it, attributable at least in part, I think, to the simplistic notion that if *they* can't understand how we know of the ET's existence, neither can science. There will be people who are scared by it -- many of whom will become hostile or paranoid and act out in any number of ways.
There will be religious fanatics from all different denominations who will somehow (negatively or positively) associate the beings' existence with the god of their choice. Some (but certainly not all) people of faith will suddenly ask themselves why the Bible and other man-centered documents of theology do not mention these other creatures, which they will have to assume were *also* divinely created or, perhaps, are freaks of nature (which will then re-raise the question, "Then why not here? Why, if you think spontaneous life is possible, can you not accept that it happened *here*?") The whole evolution "debate" will be inflamed.
There will be UFO enthusiasts who will beam with pride, saying "I told you so" despite the fact that they have not generally (in fact ever, to my knowledge) provided any hard evidence of alien beings visiting earth! (Quick disclosure: I believe extraterrestrials must exist; I just don't think they come to earth every few weeks -- if ever!)
There will be sheer delight in the science community -- especially among the exobiologists -- who have made the seeking of such beings their life's work.
But above all, it will immediately change our perspective from one of a single lonely life-harboring oasis surrounded by vast emptiness... to one of an equally vast space in which we have company... and if on this other planet, why not on many more? The notion that we are an entire cosmic collection of beings will finally hit some people.
When and if that happens, and if we're still around, just maybe rationality will win over nation-centric, religion-centric, and politically divisive attitudes, and the bulk of humanity will see us all as the same, more than different... that we are all part of ONE (human) family. Just maybe.