Product group is the third classification term for parts, and is mainly intended to assist you with default coding for customer orders and purchase orders.
Other secondary uses of product groups is Discount Categories, and to use them as classification / selecting terms in lists over purchasing and sales statistics.
If you click on the button 
next to the Product group field you can see (under the tabs Sales, Purchase and Subc.) the part's link to the product group in the product group matrix as well as the coding on account, cost center, cost unit, project and project cost type. When coding on sub-objects you will also see if the sub-object is mandatory or not.
The information shown under the Subc. tab is determined by the setting Subcontract Coding via Product Group on under the Accounts Payable under the Purchase tab. If the setting is set to Main part you will see the same information as under the Purchase tab.
You create product groups in Product Groups in the Global Settings module, and in that procedure you enter which income or expense account will be used by default for each customer or supplier during order registration.