The bands are called "headbands." (Sometimes only the top band is called a "headband," while the bottom one is called a "tailband." This distinction is apparently less common today.) According to this page, most headbands are "ornamental," though some are "functional" in older books:
"When the headband is an integral part of the book, it serves the practical purpose of taking up much of the strain from the spine covering when the book is pulled from the shelf in the usual manner. ... The headband that is only glued on, on the other hand, is merely decorative ...."
(Bookbinding and the Conservation of Books: Dictionary of Descriptive Terminology: headband)
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