What it's about, briefly: A boy named Ged learns the ways of life and magic, and in addition to learning how to use magic he also learns when and whether he should use magic.
The slightly longer version...
A village boy has an unusual gift for magic, and his skills become particularly apparent when he saved the people of his village from raiders by confounding them with weather magic. A wise old man takes Ged under his wing to teach him, but ultimately Ged chooses to learn the art of magic at the wizarding school on Roke. It's there that, through anger and pride, he looses a shadow that would destroy him and others. But more on that shadow in a bit.
There are a few things I really love about this book, just one of which is that it's the beginning of Ged's story (the rest of which are told in the other Earthsea books). And of course, there are the dragons. That's typically enough to keep me happy.
I'm also fascinated by how the book portrays magic and discusses the balance of the world. In my latest reading it seems reminiscent of Star Wars, though I'm not sure if I could explain it at this point in time. (FYI this book predates Star Wars. I checked.) The following paragraph is a brief summary of the nature of magic and the world.
"All power is one in source and end, I think. Years and distances, stars and candles, water and wind and wizardry, the craft in a man's hand and the wisdom in a tree's root: they all arise together. My name, and yours, and the true name of the sun, or a spring of water, or an unborn child, all are syllables of the great word that is very slowly spoken by the shining of the stars. There is no other power. No other name" (164).
Yep, on to spoilers time now. Brief note: with a true name you can control a person or thing. Everyone and everything has a true name, but people keep theirs hidden.
What really fascinates me is that the shadow Ged looses is ultimately himself. But of course, it takes him a while to learn this. He loses his anger and pride when it arrives, which were the reasons it arrived in the first place, and they are replaced by self doubt and meekness. That is, until he realizes the danger he and others are in if the shadow catches him. At that point I don't know if he searches for ways to fight it more for his own sake or others, but even if he is meek in some cases he certainly has no trouble facing danger when and where necessary.
Ged finally realizes that the shadow is a part of himself and in their final confrontation speaks his own name, which is also the shadow's name. And so, far from trying to destroy the shadow as he had intended when he first set out, he has embraced it as part of himself. It seems to me that it's at this point that Ged truly comes into his own.