Providing you include more than one, the iOS device will look for the correct size and utilise that image automatically. As you can see from the names of the images in the example, the iPad with retina display needs an icon which is 144x144px, the iPhone 4/4S/5 needs an icon which is 114x114px, the original iPad (and iPad 2, as the screen resolution is no different) needs an icon which is 72x72px, and the original iPhone doesn’t need a size specification, but for your reference it is 57x57px.
A common practice is to create a single 180x180 icon, which is the highest expected resolution, and let the iOS devices scale it down as needed. It is declared with:
Note that iOS looks for URL like /apple-touch-icon-76x76.png, if it does not find interesting stuff in the HTML code (a bit like what IE is doing with /favicon.ico). So it is important to keep the file names are they are above. It is also important to consider that Android/Chrome is also using these pictures.
You might want to know that this favicon generator can create all these pictures at once. Full disclosure: I'm the author of this site.
You may want users to be able to add your web application or webpage link to the Home screen. These links, represented by an icon, are called Web Clips. Follow these simple steps to specify an icon to represent your web application or webpage on iOS.
To specify an icon for the entire website (every page on the website), place an icon file in PNG format in the root document folder called apple-touch-icon.png
To specify an icon for a single webpage or replace the website icon with a webpage-specific icon, add a link element to the webpage, as in:
In the above example, replace custom_icon.png with your icon filename.
To specify multiple icons for different device resolutions—for example, support both iPhone and iPad devices—add a sizes attribute to each link element as follows:
The icon that is the most appropriate size for the device is used. If no sizes attribute is set, the element’s size defaults to 60 x 60.
If there is no icon that matches the recommended size for the device, the smallest icon larger than the recommended size is used. If there are no icons larger than the recommended size, the largest icon is used.
If no icons are specified using a link element, the website root directory is searched for icons with the apple-touch-icon... prefix. For example, if the appropriate icon size for the device is 60 x 60, the system searches for filenames in the following order:
apple-touch-icon-76x76.png
apple-touch-icon.png
See Icon and Image Sizes for webpage icon metrics.
Note: Safari on iOS 7 doesn’t add effects to icons. Older versions of Safari will not add effects for icon files named with the -precomposed.png suffix. See First Steps: Identifying Your App in iTunes Connect for details.
Since a few of these answers are out of date already, I recommend using http://realfavicongenerator.net/ to generate all the images and markup - I donate a couple euros each time I use it in the hope that it enables them to keep up to date as to what is currently valid on iOS, Android & Windows, so I don't have to.