A somewhat dated word for the opening of an exhibition. The term was once an almost direct translation from the French word Vernissage, and its meaning has changed over time.
Today it means the viewing of art in the form of an afternoon or evening reception e.g. at a gallery. In the past varnishing/vernissage was granted to artists the last day before the opening of an exhibition allowing the artists to do the finishing touches to their paintings and seal them in a coat of varnish.
Usually, this coincided with art critics being invited to see the art on this last day before the public viewing.