Reprinted from a blog entry by toddesplin here:  http://community.mozy.com/t5/Community-Blog/How-do-I-know-if-Mozy-is-working/ba-p/30415

A common question we hear from new customers is "How do I know Mozy is working?" The answer is surprisingly simple: "Mozy is always on, working away in the background . . . unless you turn it off." Mozy is a service that can run while your using your computer or when you are away from it. Although you may not see all that it does, it's working hard to protect your files. 

Mozy is designed to keep track of the files that need to be backed up and then perform the backup at the scheduled time. Even if you set your scheduled backups to run once per day, Mozy will be collecting the information it needs throughout the day to run the backup. If there is a problem that prevents Mozy from starting or completing the backup, Mozy will alert you about the problem and try to run the backup again. If the problem persists, Mozy will let you know what you can do to fix the problem yourself or how you can get help from a Mozy customer service representative.

There are several features you can use to help you find out what Mozy is doing at any given time. Below, I've listed a few things you can do to see Mozy in action.