It's the main executable of WakeMeUp! software that provides an interface for manipulations with your alarms. It is the only program you need to run to completely configure WakeMeUp! system on your machine.

WMUSvc.exe is a system service. It starts along with other windows services, such as network support or WinXP skin support. This program doesn't require a user to be logged on. Actually, this program fires all alarms of WakeMeUp! system. It has no interface and can be completely configured by means of WakeMeUp.exe

A user-mode invisible program used by WakeMeUp! System Service to run alarm notifications and command lines in the context of alarm owner user account.

The program that notifies you of your alarms. It can play a sound (mp3,ogg,cda,wma or wav), display a message or make beeps by means of PC speaker.

Let's briefly describe the scheme above. Every user of your PC for whom WakeMeUp! is installed is allowed to create and manage his own alarms. It's very important to point out that a user can manage only his own alarms. In spite of it any user can see the immediate alarm, no matter whose it is.
Another important point is that WakeMeUp.exe is responsible only for providing an interface for alarms management. It doesn't fire an alarm itself. Therefore, you need to run it only when you want to configure or reconfigure your alarm list. And, by the way, it is the only program you will ever need to run!
WakeMeUp! system service (WMUSvc.exe) is always running. It doesn't consume much resources and therefore you can forget about it. Actually, it is the main component of WakeMeUp! software. It is responsible for managing alarms from multiple users and starting alarm notifier (Informer.exe) when required.