Veracity sounds like some kind of disease you don't want to catch, but in fact, it means truthfulness. If you question the veracity of a statement or story, you wonder whether it is truthful or accurate.
Veracity is linked to the adjective veracious or "truthful." But don't confuse veracious with voracious. A voracious person eats very large amounts of food. If you were veracious, or "truthful," you'd tell them they look fat.