Both Uses of

demonstrate
in
To the Lighthouse

Scolding and demonstrating (how to make a bed, how to open a window, with hands that shut and spread like a Frenchwoman's) all had folded itself quietly about her, when the girl spoke, as, after a flight through the sunshine the wings of a bird fold themselves quietly and the blue of its plumage changes from bright steel to soft purple.†
Part 1 *

demonstrating = showing

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