A good example is an image used as an icon next to a text label. Imagine a link/button that contains the words "Save" and a floppy disk icon. There's no need to have an alt of "Save" on the icon as the text "Save" is already present. So it would look something like this:
<a href="#"><img src="save-icon.png" aria-hidden="true">Save</a>
Though in this case you'd probably be using an icon font like FontAwesome.[1] https://stackoverflow.com/questions/31107040/whats-the-diffe...