If you already have a Joomla website you are probably interested to make sure that the site works on a mobile device. Mobile devices have unpredictable screen sizes and the speed of the internet connection can be low. The loading of images can take longer. The Abobe Flash player does not exist on all devices manufactured by Apple, and on other platforms it can cause problems in the sense of speed and stability. Advertisements are hard to display on mobile devices and last but not least, the layout of the websites desktop versions can be too complex for mobile devices.
Separate Mobile Website
In this case, the mobile version is a totally independent website with another URL, mostly the subdomain "m.". With extensions like Mobile Joomla it is possible to use your existing content to create a separate mobile version.
Responsive Web Design tries to adapt the layout to the viewing environment, and probably also use flexible images. Have a look at the chapter Responsive Webdesign.
The mobile version is a downloadable app with access to your Joomla website. With extensions like Chimoora you can use your existing Joomla website.