Why a private OpenSim grid?
A private OpenSim grid allows you to give your educational institution or company it's own virtual world home. You have full control of your own virtual world. You can define all rules for your world and it's users. Your OpenSim grid can use it's own domain name and grid web site (have to be bought separately).
Why an OpenSim standalone region?
OpenSim standalone regions are independent tiny virtual worlds ("mini grids") running on a single OpenSim process. Up to 4 regions can be installed, although for optimum stability it is recommended, to just run one region on a single OpenSim process.