Notifications are a way of letting one or more people know that an event occurred. An event in Campaign Master can be a number of things, the most common being a form submission.
If, for example, you had a form to allow people to accept your invitation to an event you might want several things to happen automatically. For example:
Send an email to the event co-ordinator letting them know of the form being submitted.
Send an email to the recipient's account manager so they can make a personal phone call.
Send an email to the recipient letting them know that their acceptance has been received.
Update the database field "Accepted" to "Yes" so you don't send them a reminder in the follow up campaign you have planned.
There is no limit to the number of notifications you can set up and no limit to the number that can be applied to a single event.