A couple of automatic ways exist if I am understanding your question:
As a website preview this sounds like snapshots. These are enabled by going to Design>Extras then you can click on snapshots. This will give the little preview of what is behind the link in either sidebars or in posts.
As for other mouse overs it is possible to have this in links in the sidebar. Go to Manage>Links and choose a link to edit and fill in the description part and save it. This will make the message you entered in the description appear when someone rolls over your link.