Anonymous surfing sounds like some new California way to surf the big waves while wearing a ski mask, or something like that. But no, it refers to people surfing the Internet anonymously. Of course, that begs the question: why on earth would anyone want to do that, what is the point? It is done for two reasons: first, you may not want the web sites you are browsing to know who you are; and second, you may want privacy from anyone who might be watching your network connection. That can include the government, your employer, or nosy friends and/or family members. They can log into every access you make, every site you go to, even every picture and/or video you download.
The system works by the use of what could be called a “middle man.