Very important for internet marketing / search engine optimization (SEO). An alt tag is the HTML text that appears when a cursor is positioned over an image or sometimes when an image is loading. Search engines can read an alt tag that accompanies JPEG/GIF images. Every relevant image should have an alt tag. The text in an alt tag is believed to be given additional weighting.
However, don't forget the title attribute in the image tag and don't forget that Internet Explorer 8 and below does not show the alt attribute when hovering over the image, yet it does show the title attribute.