User Agent switching is a technique to change your desktop browser user agent string (HTTP User agent header) which identifies your browser and device.
Web browsers allow you to switch this string. This allows you to see how your site produces HTML code for mobile devices, making it possible to develop and debug mobile themes easily. However, it will only allow you to see HTML source code - it does not magically change your browser rendering engine to mobile browser.
It is good to test many browsers or user agents. If you do not have several devices in your possession, please see our blog series on testing mobile websites on desktop. For a quick check, you can download User Agent switcher extension for Firefox and test your site using e.g. iPhone 6 user agent (this user agent string is prepared and comes with UA switcher).
You can also use Mobile Joomla's user agent helper service to see the current user agent of your browser.
Mobile Joomla! uses user agent database called Wurfl to identify mobile devices. You can browse from available test user agents from Wurfl site.