A demonstrative is a form that either has among its uses a meaning that contrasts with some other form in terms of physical proximity to the speaker, so that there is at least a two-way contrast of proximal (near speaker) versus distal (not near speaker), or the form has among its uses an indication that the hearer is intended to direct their attention towards something in the physical environment.
In many languages, demonstratives also have anaphoric uses, i.e. they refer to entities that were mentioned earlier, e.g. Last year we bought a cat from our neighbour, and this cat has become a true member of our family. It is from such anaphoric uses that demonstrative often develop into definite articles, and often they are not easy to distinguish from them. (See APiCS Glossary under “definite article.)
The term apparently goes back to antiquity and is attested in English since the 16h century. It is based on latin demonstrare 'show, demonstrate'.
- Diessel, Holger. 1999. Demonstratives. Amsterdam: Benjamins.