Let's start with the definition. An ex-library book is a book that once belonged to a public library or institution and has been 'discarded' after being deemed no longer useful. These books often gravitate into the hands of used booksellers and end up for sale on online marketplaces such as AbeBooks.
A 'friends of the library' sale is also the obvious place to find ex-library copies and an excellent way to support a worthy cause. It's important to remember that a book described as ex-libris is something different. Ex Libris, a Latin phrase, means "from the library of" and describes a book that comes from a personal library.
An ex-library book will carry some sort of marking indicating the name of library that previously owned it. It could be a stamp, or a barcode label, or an 'old school' pocket for the checkout card. It will also probably carry some sort of stamp bearing the word 'discarded' or 'withdrawn', or the barcode has been obscured with a pen.
Sadly, ex-library books have a poor reputation because an old library book can have many miles on the clock and there is also a lot of them available online. It's true that they may have been read numerous times. However, remember publishers produce 'library editions' with sturdier bindings to withstand being handled and reshelved many times.