The Databases A-Z tab is simply an alphabetical list of all the databases available in GALILEO. You can see the entire list, type in the name of a database, or click on the first letter of a database title to see everything that matches that letter. You can also use the search box to type in a keyword and pull up any databases that pertain to that term, for example "statistics" would pull up every database that contains that term in its description. This is a great way to find databases if you aren't familiar with database titles.
There is also a link on this page called Express Links which gives you the persistent URL of all the databases in GALILEO. You can copy and save these links so that you can access the databases directly whenever you need them.