A Property Group is a way to categorize Dimension Members according to attributes that need not be unique, as Aliases must be.
As an example, there may be a Customers dimension that has 50 different companies who buy products from our firm. We wish to identify the title of the contact person for each company.
ContactPersonTitle could be the name we give to the Property Group; and the title would be an attribute for each company–possibly 25 of those could share the title Purchasing Agent.
In this example Purchasing Agent would be the Property, say for Acme Company, alerting us to the fact that the contact person we need to reach is the Purchasing Agent