The one use I know of for Construction Groups is in conjunction with BMX (the Behavioral Modeling Extension) in order to create a UDA (User Defined Analysis).
Off the top of my head, a Construction Group is a Local Group that performs a calculation. It will typically have a Field Datum Point as the first feature, and a Datum Analysis feature as the last. It will typically contain other datum and surface features in between; it can have solid features, but I personally have never seen or done that.
The UDA performs a custom analysis on the Construction Group for every possible value that the Field Datum Point can have. (A Field Datum Point is an underconstrained datum point defined as existing somewhere on a specified curve or surface.) UDA's require Construction Groups.