To be folded in a manner like the ear of certain dogs. It implies the page was purposely folded to mark the page:
By thumbing to the dog-eared pages, she quickly found the items in the catalog she wanted to order.
To be bent or slightly ragged in appearance in a manner like the ear of certain dogs. It implies that the page has been read a lot, but could be a sign of mistreatment:
The pages in his favorite book were dog-eared from years of reading it at bedtime.
A book or piece of paper that is dog-eared has been used so much that the corners of the pages are turned down or torn. dog-eared copies of ancient history books. dog-eared books or papers have been used so much that the corners are turned over or torn