First the story, without spoilers: astronaut Frank Poole's body is found after 1000 years in space in the outer rim of the Solar System. In 2001 he was left for dead in space by Dave Bowman, the other astronaut of the famous spaceship Discovery we get to know in "2001". In the year 3001 it is possible to revive Poole, because he was in a deep freeze vacuum. So Frank awakens in a whole new world, makes new friends and learns more about what has happened in the past millenium. But finally he wants to go back to Jupiter and find what may be left from his old friend Dave Bowman...
This sounds like a very promising story. But while it starts fine and is better written than 2061, the book ends in a disappointing, rather anti-climatic and much too simple way, which somewhat destroys the fascination found in 2001. In general: while 2001 is a work of two geniuses (Clarke and Kubrick), 2010, 3001 and especially 2061 are never reaching the heights of their predecessor. Maybe Stanley Kubrick was the one who gave 2001 its intense and mindblowing dimension, that is mostly missing in the sequels.
If you like othter books by A.C. Clarke, whom I consider a very good science-fiction writer in general, and if you really are a fan of 2001, then read this sequel (especially if you have fought your way through 2061).
But to everyone else: if you want to understand 2001 better - watch the film again, read the novelization. 3001 will bring you nothing spectacular.