Title Attribute
The title attribute is very important for users who are handicapped. It gives them a means of seeing the words clearer, and also adds a description to a link or image you wish to use.
Use on an image
Many webmasters are using the alt attribute as a popup description of an image, however this is not its original purpose and only works if the visitor is using Internet Explorer (or has extensions). The popup should be done as a title attribute instead, an example of this is: <img src="image.jpg" alt="an image" title="A walk across the sunset">. In this case when a viewer leaves their cursor ontop of an image they will see a popup stating "A walk across the sunset."
Title attribute for a link
Some links just need more information, or possibly your site has handicapped visitors quite often and you need a better way for them to read the anchor text. In either case, you should use the title attribute. An example on how to do this would be: <a href="http://www.myspace.com" title="A place to meet new people">.