Reading copy is also used by used booksellers to refer to a book that is in such poor condition that it's only value is as something to read right now - the condition is too poor to be of any long term value - not the copy you want to buy to collect.
A book that is described as a reading copy will often have the binding coming apart, some damage to the cover, probably be missing the dust jacket. The exact condition will depend upon the specific title - on more valuable titles, more damage is acceptable while still having the book have some value.
A reading copy will not be pretty, but it may be a way to get a book that would normally be a $100 book for $3 or $5.
"Reading copy" generally implies that the book is not worth rebinding. A book in this condition that is worth rebinding is called a binding copy.