The Babylon Search toolbar is frequently categorized as a browser hijacker because it takes control of the Web browser and does things the user may not have specifically requested. For example, even if you set your "home" page, Babylon will display its own site. Or when you try to get to Google or Bing to perform a search, the browser will redirect to Babylon Search (search.babylon.com). A toolbar will also appear at the top of your browser window.
It's technically not a virus, but it does exhibit plenty of malicious traits, such as rootkit capabilities to hook deep into the operating system, browser hijacking, and in general just interfering with the user experience. The industry generally refers to it as a "PUP," or potentially unwanted program.