There are two types of dismissal:
Permanent: If a Notification is dismissed by a registered user it will never show until such a time that they reset their own dismissed Notifications (in the Account Preferences page) or you Reset a notification which will force it to be shown again regardless of whether it has previously been dismissed. This is activated by clicking the "Dismiss Notification" link.
Temporary: Temporary dismissal is activated by the "X" in the top right corner of the Notification. When you close a Notification, a cookie is set in your browser that will prevent the Notification from showing for X days. X is defined for each Notification. If X is set to 0 then the Notification is hidden for the current browser session only (so restarting your browser will bring it back).
If you disable both of these then the Notification can still be closed... (Think about how annoying it would be if the Notification was covering the "Post Reply" button, for example) but the Notification will display on every single page load.
Permanent: If a Notification is dismissed by a registered user it will never show until such a time that they reset their own dismissed Notifications (in the Account Preferences page) or you Reset a notification which will force it to be shown again regardless of whether it has previously been dismissed. This is activated by clicking the "Dismiss Notification" link.
Temporary: Temporary dismissal is activated by the "X" in the top right corner of the Notification. When you close a Notification, a cookie is set in your browser that will prevent the Notification from showing for X days. X is defined for each Notification. If X is set to 0 then the Notification is hidden for the current browser session only (so restarting your browser will bring it back).
If you disable both of these then the Notification can still be closed... (Think about how annoying it would be if the Notification was covering the "Post Reply" button, for example) but the Notification will display on every single page load.