Browse can mean either to read in a rather unmethodical manner or to look through items for sale or a collection in a similar manner. Imagine you're in a bookshop which has a massive sale on and you keep flitting between titles by your favourite authors and pretty, shiny notebooks.
Another meaning of the word browse is vegetation eaten by animals and their method of consuming it. A browser is someone who browses.
So, you could browse the library for a book on browsers browsing on browse, to browse through. (If that scrambled your brain, blame Hilary - the word was her suggestion.)