Just to add a bit to what skiroomalum posted, the edition of a book is defined by it's content. If no changes are made for a second printing, that's technically a first edition, second printing. In terms of collectibility, you are generally, except in a few cases, interested in first editions, first printings. Of course, if Buk signed a later printing, then the book will have value to a collector. The only Black Sparrow book of Bukowski's that has a true second edition is Women, as a result of some editing that was done that Bukowski found out about and rectified for the second printing. Several non-Black Sparrow titles have had multiple printings, including A Bukowski Sampler, Fire Station, and Poems Written Before Jumping Out of an 8 Story Window, to name a few. In these cases, the first editions are worth more, but the second editions are still very collectible, and are generally worth somewhere in the neighborhood of 30-60% of the first printings in comparable condition.
Edit: Or, what Bill said...