When you click on the Alert widget on the database dashboard, the database alert page showing pending alerts for the database will be displayed.
After you review the alerts and take any necessary action for the selected database you can clear the alerts for this database.  To clear the alerts click the bar graph icon to the top right.  
In this section of ACP you can also Manage your subscriptions for this database only, by clicking the My Subscriptions tab at the top.  If you would like to add an alert subscription, click the plus sign in the right corner.  Then a pop up will appear that will allow you to select the new alert you would like to receive.  Remember to check the enable check box and then click save. Subscriptions added here will be for this Act! database only. If you wish to add an alert subscription to all of your Act! database, you can add this in the Settings option under the account menu.