So, what's the fuss about?
Covenant isn't "Tolkien with the serial numbers filed off." That it holds together with a complete fantasy story in a clear, magical fantasy world and you never once want to compare it to Middle Earth is a good enough start to recommend reading it. Covenant is a fantasy The Stranger, taking a disaffected character who denies all responsibility in his life and feels completely disconnected from the world around him and giving him the power of life and death.
The character Thomas Covenant is definitely unappealing. I put the book down and had to restart it 3 times after a scene in the first book where he—refusing to believe that the woman he was with was anything other than a dream—committed a rape. The morality of how you treat not-real people is a regular theme of Donaldson's and this is his first and harshest demonstration of the subject. It's not easy to read and it's not easy to go on with a protagonist like that.
Watching him slowly learn guilt, remorse, and repentence takes the next two-and-a-half books. As many people comment, that portion of the story is a downer.
Alongside the moral tale we have the fantasy epic: a modern American man returning to a fantasy world (The Land) several times seeing the consequences of his involvement in their epic battle against their own satan-figure: Lord Foul, who wants to break the Arch of the World and release himself into our universes.
Everyone in The Land believes that Covenant is the "White Gold Wielder" who carries power strong enough to break the arch or to stop Foul. This sets up the fantasy/action story, where the people of The Land try to convince Covenant to learn to use his powers and to use them for the greater good and Foul tries to get the power.
Since Covenant only visits The Land when he's suffered a head injury or some other strange type of sleep, he believes The Land is a fantasy of his own imagination.
The people in The Land don't understand why he doesn't believe in them, but they do see how broken he himself is and realize that he won't be able to help them unless he heals from his personal traumas and builds some positive self-concept.
It's a strange twist on the "apprentice who just needs confidence" trope and his mistakes during the early period are all the more appalling because he doesn't feel guilty.
Throughout the book, there is not one scene in The Land that doesn't include Covenant. At the end, we are left with no proof one way or another that The Land is a real alternate world where Covenant travelled. Perhaps his Unbelief at the beginning was correct. The existential element of the story asks why we care which is real; he does what he does and the morality comes from his making the choices.
That's heady stuff for a lightning-bolt-slinging fantasy series and it's not for everyone. It isn't modern "dark fantasy" with supposed anti-heroes who are just ashamed of being good at heart, it's real fantasy where the character development is on as epic a scale as the good-vs-evil plot.
This isn't bus reading and no book is right for everyone, but it's an audacious and brilliant series that flexes fantasy's power to drive character. It's also a fun read with the single scariest magical nasties in the genre (the Reavers).
The second series? It's different on the moral tale while following the same general plot arc, showing how the character involved changes the story. Not worth reading for everyone, but worth a shot if you like the first or if you are interested in the structure of fiction.