Definition: Tools that are described as broswer-based run on your web browser (such as Firefox, Internet Explorer or Chrome, for example). This means that it doesn't matter which operating system you are using on your computer, as browser-based applications only require on an Internet connection and a web browser in order to run properly.
One of the main benefits of browser-based applications is that there are no downloads necessary in order to make them run. This means that, generally, even users behind firewalls can benefit from using these types of tools. Why do we call them Web apps? The difference between browser-based software or Web apps and websites of yesteryear (pre Web 2.0) is that browser-based tools provide desktop-like application functionality; cloud computing technology makes working online using just your Web browser feasible.