Spiritual Meaning:
When we take part in a public demonstration we are declaring our allegiance to a belief or ideal.

Psychological / Emotional Perspective:
To demonstrate is to prove conclusively that something is possible. Often we will dream of a solution to a problem that proves to be workable.

Everyday Material Aspects:
When we find ourselves demonstrating a skill that we did not know we have, it suggests a strand of creativity that needs to be explored.

You might also like to consult the entry for Procession.