Event Groups are used for grouping multiple performances into one "group" to be used in Packages.
Ex: You want to sell a package where a customer can choose to go to any 1 of the 15 Shrek performances, and have that count as 1 event in the package. You would simply create an Event Group called "Shrek" and assign all the performances to that group.
Tip: While creating an event, this field can be left blank if you don't have multiple performances or packages.
If you have any more questions about the use of Event Groups see Packages.