Real Dictionary

demonstrate
verb: If you demonstrate a particular skill, quality, or feeling, you show by your actions that you have it.
verb: If you demonstrate something, you show people how it works or how to do it.
verb: To demonstrate a fact means to make it clear to people.
verb: When people demonstrate, they march or gather somewhere to show their opposition to something or their support for something.

demonstrate in American English
to show by reasoning; prove
to show one's feelings or views by taking part in a mass meeting, parade, etc.
intransitive verb: to make, give, or take part in, a demonstration
transitive verb: to make evident or establish by arguments or reasoning; prove

demonstrate in British English
verb: to show, manifest, or prove, esp by reasoning, evidence, etc