@Anonymous
What does parametric mean,
Parametric will have different meanings depending on the context. I will assume for the moment that you are refering to the mechanics of the software package and not in terms of architecture or design.
and how does the parametric change engine keep
everything updated when I make changes?
That would be a better question for the Revit API Forum. But here's a link to the wikipedia article on the origin of the name Revit: Wikipedia.
Why is the concept important?
Ah, a better question question for this forum. From the history section of the Wikipedia article you will note that:
"At the heart of Revit is a parametric change propagation engine that relied on a new technology, context-driven parametrics, that was more scalable than the variational and history-driven parametrics used in mechanical CAD software.[4] The term Parametric Building Model was adopted to reflect the fact that changes to parameters drove the whole building model and associated documentation, not just individual components."
As related to the task of modelling a building, non-parametric software will create a static model requiring the user to effect all changes intentionally. With software that includes parametric components, the updating of these components by changing the values of the parameters is a combination of time savings and respecting the design intent that is incorporated in the algorithms the user has embedded in the parametric components. When the entire (or close to - some things can't be parametrically driven) model is parametrically enabled, which is the case of Revit, the efficiencies and parametric design possibilities are scaled up considerally.
At this point, it would useful to include the concept of parametric design in the discussion as well as come back to "how does the parametric change engine ...". I would propose that there are three types of parametric interactions: a "fixed - hard coded" set of parametric operations, an "open" system of families and a "computational" functionality thru the API and the use of Dynamo.
But that is a more philosophical question.
-luc