Since medieval times, having books was a serious status symbol and a demonstration of wealth. As time wore on and books became more popular--and especially with the dawning of the printing press (allowing for mass distribution and lower cost) and the development of the novel--it became a common community practice to share books. Of course, it was then difficult to retrieve the books or keep track of them, so people would print or stamp their family insignia within them before lending them out. Thus the modern library stamp was born.
Aside from introducing a book into a collection and establishing it as part of that collection, a home library stamp is elegant, classic, timeless and something that posterity can appreciate. It personalizes a book in a rare way, and allows for sharing without concern of theft.
Some of the more common phrases, other than a stamp that just says "______ Family Library", are "Ex Libris," Latin for, "From the Library of ___," "This Book Belongs To..." or possibly, though slightly inaccurate, "From the Desk of ___."
You can purchase these stamps at most places that will let you customize your own stamps, like Staples.com or SimplyStamps.com, and you can usually have them customized not only according to your text preferences, but you can give them/upload a graphic like a family crest or seal to have them inked with as well (see Resources below).
Like most things associated with books, this is just one more thing that has the potential to get people more interested in sharing and reading books, especially children. Any way that you can make a child feel like a book is really theirs and is relevant and important in their life is a positive step.