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Remote Desktop mobile apps allows you to use the applications on your office computer, and access your data without being in your office. It is absolutely helpful for business, where the person can access the intranet from his mobile phone when he/she is out of the office.
I only use it for checking on things at home when I'm at the office, or for restarting servers at the office when I'm performing maintenance late at night. I'm not using my iPad though, I'm using my Mac. I prefer having a bigger screen when I need to control the cursor on a Windows 2008 box.
Administration: pretty much for the same reason you have command line access on many Unix devices. When you have Operations centre, and servers or stations spread around the globe, or just in a different room. If you are not allowed to physically enter premises. Not to mention it's more comfortable to configure or install something from your comfy chair than spending many hours in cold loud datacenter. Plus, when you have modern blade servers (chassis + boards with processors) they don't have monitor and keyboard ports on each physical piece of hardware - if they have any at all.
Virtualisation: how would you efficiently connect to and manage X virtual servers running in one physical computer? Not to mention somewhere "over there in cloud"?
Training: to online demontrate user how to do certain things right in front of his/her eyes
Laziness: this does not need further explanation :-)