A first edition, first printing book is the original content and it is from the first print run.
A first edition, second printing is a book with the original content unchanged and is from the second print run.
A book that has had at least 20% of its content changed can be called a second edition. The first time this version goes to press it is a first printing of the second edition.
A book that has unchanged content can be printed an unlimited number of times. In the case of a very popular book (like the Harry Potter series) it is possible to have a first edition book with a high printing number.
First edition, first printing books are the most rare in collectible books. However, in today’s prolific printing industry it is quite common for books to never make it to second printing thus ensuring there are a lot of first edition, first printing books on the market.