Modern mobile devices like iPhones, iPads and Androids boast high-speed web access and fully-featured browsers. They also have the ability to add a frequently visited site to their home screen as an icon. If you want your site to be represented with anything more than a generic picture or a zoomed version of your site’s 16 x 16 pixel favicon, you need to create an image with a very particular size and filename.
That image must be in PNG format, exactly 114 × 114 pixels in size, and have the filename apple-touch-icon.png or apple-touch-icon-precomposed.png. I recommend using the latter, as images with that filename are picked up by both Apple and Android devices, and escape a “shine” effect when they are rendered on the device’s screen. You can see the icon for this site in the top left corner of the image to the left.
You should treat the home screen icon image exactly like a favicon, and upload it to the root of your web server, directly beside the index page. No changes to your HTML code are needed: devices will pick up the icon automatically.
(And yes, the screenshot is from one of my own Apple devices: to take a screenshot under iOS 5, simply hold down the sleep button and tap the home button twice. The resulting screen grab is saved to your device’s camera roll.)