A demonstration is a show, or display. If you are against war, you might go to an anti-war demonstration in front of the White House. You might need to see a demonstration of napkin folding before you take a job as a waitress.
Dressing well for a job interview and showing up on time is considered a demonstration of your seriousness about the job. Crying is a demonstration of your feelings. If you sell website design you can make a demonstration site, or demo, so clients can see what they would get if they hired you.