A recent survey of attempts to request nonexistent files on web sites found that the file which was most frequently requested was apple-touch-icon.png. That is the name of the icon which will appear on an Apple device when a bookmark for the site is saved.
Because this is a bookmark icon, someone has decided that your site is worth bookmarking, and their device is looking for an icon to represent your site. You probably want your site to look as nice as possible to them, so your webmaster probably should define an Apple-friendly icon for the site.
There actually are several sizes of icons which can be defined. Details can be seen here in an Apple web page.