Anonymous web browsing is browsing the World Wide Web without making one's IP address or any other personally identifiable information available to the websites that one is visiting.
A degree of anonymity can be achieved by using a proxy server. If the proxy server is trusted, anonymity will be retained because only the information on the proxy server is visible to outsiders.
Anonymous web browsing is generally useful to anyone who wants to ensure that their sessions can not be monitored. For instance, it is used to circumvent traffic monitoring by organisations which want to find out or control which web sites employees visit.