Event Calendar scripts are a type of web-based database software which allow you to create, modify, delete and move multiple calendar event descriptions, and have them displayed in different calendar formats (ie, traditional monthly grid; list view; day view; and numerous other variants).
There are quite a few script formats to choose from. Two of the more popular calendar scripts are called (simply enough), CalendarScript and WebCalendar, both of which are powerful, flexible, robust and extremely customizable.
WebCalendar is more feature-laden out of the box, and utilizes a more powerful MySQL/PHP solution, but CalendarScript has a bevy of third-party plugin scripts which allows it to be tweaked beyond it's integrated features.
Screenshots of each calendar can be found below: