How to notify user in ios while application is closed / inbackground

I want to notify the user of the "time".

eg:

I have a table view with many rows. these lines resemble reminders, where the user can set the date and time of the reminder.
Therefore, the reminder line is set on April 24 at 12:15.
The application is closed at this time.

So, how can I notify the user that this time?

Is there any way to do this without the push push notification service?

Edit 1:
Thanks for the answer, here is an example of local notifications :

//This example adds 20 seconds to current time, use it for testing 
    UILocalNotification *localNotification = [[UILocalNotification alloc] init];



    NSDate *currentDate = [NSDate date];
    NSDate *currentDatePlus = [currentDate dateByAddingTimeInterval:20];

    localNotification.fireDate = currentDatePlus;
    localNotification.alertBody = @"Hallo ayFon User";
    localNotification.soundName = UILocalNotificationDefaultSoundName;

    [[UIApplication sharedApplication] scheduleLocalNotification:localNotification];
    [localNotification release];

EDIT 2:

//Add this for iOS 5 Notifications
[[UIApplication sharedApplication] registerForRemoteNotificationTypes: 
 UIRemoteNotificationTypeAlert |
 UIRemoteNotificationTypeSound];