"Connotation" means that the work of art inspires or brings about a reaction in the viewer/listener/reader of an association or relationship (emotional or otherwise) to something outside the work of art. It may be an emotional response where the viewer feels an association with an event in his or her own life; it may be a mental association of the artwork with an historic event, or a philosophical concept; it may be the work actually refers to some real world event or cultural ideal or human condition to inspire the asociation within the viewer's mind. Puns, symbols and allusions are often used in this context.
We must first define what connotation means. According to my English teachers in middle and high school, they taught me that connotation is the association of one thing with another. In other words, when someone mentions one thing, I immediately thing of something that I can relate it with. So in terms of arts or music, I look or listen at the artist/musician's works and I relate it to moments in my life that relate with their pieces. Often times, if a song I listen to was sad, then I think of sad moments. If I look at a work of art and I feel happy, I recollect a memory that made me happy.