Mozy automatically chooses the files to back up using backup sets. During installation, you can deselect these backup sets. Your first backup has to copy all of your selected files to the server. How long this first backup takes depends on the amount of data selected to be backed up as well as the speed of your internet connection.
One way to shorten the first backup is to deselect some non-critical files for the initial backup, and then add them to your backup later on. To understand what files are being backed up, see: How does Mozy Determine What Files to Back Up?
To remove files from the backup, see Selecting Backup Sets.
All subsequent backups generally only take minutes because only the files that have changed are uploaded to the servers.