Let's get one thing clear right off the bat: Doctor Sleep is not as scary as The Shining, even though it comes pretty damn close. However, thematically it's a worthy sequel to one of Stephen King's most popular books.
With Doctor Sleep, King inverts a lot of the themes of the original novel. The Shining was about the spectre of alcoholism; Doctor Sleep is about recovery. The Shining was claustrophobic, isolating the characters in a relatively small space; Doctor Sleep is expansive, spanning the breadth of the U.S.A. Finally, while The Shining was about the stress of being parents, Doctor Sleep is about the burdens of children.
Danny Torrance, the little boy from The Shining, is now grown up and his life is a mess. His father, of course, perished with the Overlook Hotel and his mother has died of lung cancer. Dan has succumbed to the family curse of alcoholism and is now drifting from job to job. After a horrific night involving a barroom brawl and a coke-addicted single mother, Dan finally hits rock bottom. Eventually, Dan finds meaningful work as an orderly at a hospice in New Hampshire and, more importantly an AA group to sustain him. He soon realizes that he has a talent for helping people die with ease, and at the hospice he becomes known as "Doctor Sleep."
Meanwhile, a sinister group of near-immortals known as the True Knot are travelling across the country spreading terror. Psychic vampires, they travel the country in campers as they capture kids with "the shining," torture them, and then feed off the life force or "steam" released at the time of their death. The True Knot are led by Rose The Hat, an eternally youthful and seductive woman so named for her black silk topper.
Finally, in another part of New England a young girl, Abra Stone, is displaying remarkable psychic talents. From an early age she is predicting events, reading minds and moving objects. Somehow she develops a psychic link with Dan via Dan's old imaginary friend Tony. When the True kill a shining kid Abra knows as "The Baseball Boy," the resulting psychic trauma alerts Abra to their presence - and Rose to Abra's, setting off a chain of events that lead to a showdown at a familiar location...
Doctor Sleep is less a horror novel than modern fantasy, following the "group of regular people against an unimaginable evil" plot that drove his Dark Tower books. It's also strangelt optimistic. The horror is there, but there's a positive feel to the story. It's as if King decided to give his characters a second chance: Dan is Jack Torrance if he found AA, while Abra is Carrie White if she were raised by a loving family. The novel is steeped in the language of the recovery movement, and King has clear affection for Twelve Step culture (he occasionally pokes fun at some of its excesses, but always in a gentle way). (King also shows the influence of, surprisingly enough, JK Rowling: the True Knot, with their disdain of the "Rubes" they live among, are essentially Death Eaters in tourist clothing.
As with The Shining, the true terror comes from traumas of the real world. In addition to Dan's struggles with alcohol, there's a mostly down-to-Earth but heartbreaking subplot involving Abra's great-grandmother Chetta, a famous poet at the end of her life. At heart, it's about real life can be just as scary as any ghost or vampire.
(Note: there's a Big Twist near the end, that sort of makes sense but might annoy some readers)