Browsing is when you look through information quickly, without any real intended purpose. In the context of the internet, it typically refers to utilizing the world wide web. It is an excuse to waste time, but it can also be a temporary source of entertainment, as the search bar will pretty much take you anywhere you want to go.
However, sometimes there is a purpose for browsing. You could be looking for something specific, or you could be shopping on eBay or looking at the IMDB website for movie suggestions. You could also be checking your e-mail or perusing Facebook.
Browsing also means using a web browser, which is how these sites come up. The world wide web allows people to find information without even looking at it, which is similar to looking for something on a bookshelf at the library.