Whenever you check this box, everyone this Photo Album is shared with (and if it is shared publicly, everyone who has subscribed to you) will receive a Notification on their Dashboard. Anyone you have shared your Photo Album with also be notified of any changes you make to the Photo Album. You have the choice of clicking on the checkbox next to "Notifications" to send notifications to everyone in your Share List, or you can click on single checkboxes next to individual names.
If the “Notifications” boxes are not checked, then anyone you have shared your Photo Album with will not be notified of any new changes or shares regarding this Photo Album.
Learn more about Notifications.