A Favicon (short for favorite icon) is that nifty little icon you see at the top of your browser’s tab on most web sites.
favicon.ico is a single that contains up to 3 images.
Here’s an example of a favicon we designed recently for exposethemedia.com:
|16 x 16 px||32 x 32 px||48 x 48 px|
Since favicons are so small, attention needs to be paid to each individual pixel to guarantee that your icon looks sharp in all 3 formats.
In addition to favicons, devices such as iPhones and Modern Windows based devices use their own icon format when for example someone pins your web site to their home screen.
For some additional technical information about favicons read this.