Construction history allows you to do two things:
For almost every tool, Alias gives you the option of saving the history of how an object was constructed.
Editing construction history automatically updates the object.
For example, when you use the Revolve tool to create an object with construction history, you can:
...and the surface(s) updates automatically.
Objects that have construction history are drawn in green in the default color scheme.
If a surface or curve has been built with construction history, it cannot be moved, scaled, or rotated even if its constructor objects are transformed along with it.