If you read all the way to the very end of the Harry Potter series -- and I know some people did not, because they chose to skip the "epilogue" -- then the last time you saw Harry, Ron, and Hermione, they were adults sending their kids off to Hogwarts. Harry was sending his middle child, Albus, off - a kid in the same class as Draco's only child.
Harry Potter and the Cursed Child is a form of continuation, but it is not a fully-realized novel with the sumptuous setting and details we've come to expect in Harry Potter novels. Then again, it's important to remember that this is not a novel. It is instead the script of a play in two parts. Pity the poor show-goers who got tickets for only one night and cannot see the entire play.
It came about because J.K. Rowling wrote a story, and John Tiffany and Jack Thorne turned it into a play. Which means there are slight set descriptions, stage directions, and dialogue. If you already know the world described in Hogwarts, including Hogwarts and the Ministry of Magic and more, then this shouldn't post a problem to you. You don't need the full description of Platform 9-3/4 or the Hogwarts Express or the witch with the cartful of sweets who walks its aisles, because you can already conjure all that for yourself based on your knowledge of the prior books and the bits of setting and stage directions in the pages of The Cursed Child.
I'm not going to post any spoilers, which means I won't give you much in the way of details at all, except to say that Harry, Ron, Hermione, Ginny, Draco and other characters from the original series are actual grown-ups in this book, and their characters (19-22 years after Voldemort's death) logically relate to how they were when younger, but are not precisely the same, just as occurs with real people.
This story is much more interested in the younger generation, and especially focuses on Albus Potter and Scorpius Malfoy who are, against most odds, the very best of friends. And on the adventure they undertake, which -- this being a Potter story -- turns out much different than they expected, and also manages to involve the parents in an adventure of their own: working together.
If you are lucky enough to have tickets to see this in London, then I won't presume to tell you whether you should read this beforehand or not (though I will say that I know two people in that position, and both opted to read it, since they don't mind spoilers). Otherwise, it seems likely to be a LONG time before this play arrives in the United States or becomes a movie.
So read it, by all means, just don't expect it to read like a standard novel. Because, after all, it is a play.
And this play's the thing.