What influences people’s appreciation of works of art? In this paper, we provide a new cognitive approach to this big question, and the first empirical results in support of it. As a work of art typically does not activate intuitive cognition for functional artefacts, it is represented as an instance of non-verbal symbolic communication. By application of Sperber and Wilson’s Relevance Theory of communication, we hypothesize that understanding the artist’s intention plays a crucial role in intuitive art appreciation judgements. About 60 works of fine art, representing a wide range of periods, genres and styles, were selected in the permanent exhibitions at Tate Britain in London, and rated by more than 500 visitors for goodness and understanding of the artist’s intention. Results suggest that works of art whose artist’s intention is easy to understand tend to be preferred over those with more obscure intentions, even when controlling for familiarity effects.