Both Uses of

demonstrate
in
The Notebook

"No. Just grab 'em like this," he said, demonstrating, and she smiled.
*

demonstrating = showing (how something is done)

He demonstrated quickly, making it look easy, removing the meat and putting it on her plate.

demonstrated = showed (how something is done)

Definitions:

(1) (demonstrate as in: It demonstrates my point.)
to show
The exact meaning of this sense of demonstrate can depend upon its context. For example:
- "I will demonstrate how to throw a Frisbee." -- show how to do something
- "I will demonstrate how much quicker the new computer is than the old one." -- show how something works
- "Her questioned demonstrated that she was listening and thinking deeply about what was said." -- showed to be true or proved
(2) (demonstrate as in: demonstrate to protest)
a public display supporting a cause -- usually joining with others in a political protest