It should have a flexible, sewn spine which allows the book to lie flat on a surface when opened. Less good is a glued spine, because the glue gets worse with time.
Hardback books may be printed on acid-free paper. They are much more durable than paperbacks. Paperbacks are often printed on cheap recycled paper, and have flexible, easily damaged paper covers. Hardback books are only slightly more costly to make, but are often much more expensive to buy.
Hardbacks may have artistic dust jackets, or designs printed right on the board binding.