A large cylindrical object is spinning so fast through the solar system that humans want to take a look at it before it whizzes past them. They dispatch the Endeavour to intersect its orbit and quickly discover that the cylinder is a spaceship of some kind designed by an intelligent species. Once they make it aboard Rama, the crew meticulously describe the interior of it and you should eventually get a really good feel for its construction. The novel details the crew's discoveries aboard Rama.
Seventy years after the first book, a second Rama spacecraft enters our solar system, and an expedition is again sent to rendezvous with it. They board it as easily as the first crew boarded the first spacecraft, but they soon discover a few differences between the two craft.
This book (and the subsequent ones) contains a lot character development, as they are written primarily by Lee. In this one, it doesn't seem to be going anywhere, but it takes off eventually, really.