Websites have to be ready for mobile devices of all kinds: tablets like iPads and ChromeBooks, smartphones like iPhones and Androids, coming in all shapes and sizes. Your website may look perfect on a desktop computer, but how does it look on your phone? Is the text easy to read? Do you have to scroll left-right to see the full image?
Designing a site for mobile requires understanding how mobile phones are used. The site should load as fast as possible, you should not have to scroll horizontally, and images should fit appropriately. The text should not be too small or too large, extraneous items should be hidden, and the menu bar should be accessible via a small icon, rather than taking up real estate on the screen continuously.
When testing your website, you should check on as many devices as possible, to ensure your site looks great in any size. It's important to always test by turning the screen horizontally as well.