"Famous" wants us to look—long and hard—at what we often overlook. In contrast to the ways that modern society is often obsessed with superficial and unimportant elements of celebrity and the things we usually think of as being famous, Nye puts the focus on the natural world and the simple, everyday elements of life: cats and boots and buttonholes. A big part of the everyday, of course, is the natural world around us, and Nye devotes quite a bit of her poem to the earth and all its everyday-ness.
Man-made things like pulleys and buttonholes are more 'famous' than rivers and cats because they are tools developed for specific purposes, and we use them all the time.
Nature is more famous than man because nature can undo whatever man does.