Semiotics is the theory of signs and what's fascinating about signs is that they can have multiple meanings other than just themselves. For example:
Stop = Stop, but it can also mean danger.
Semiotics are the tools, processes, and contexts that we have for creating, interpreting, and understanding the signs in our everyday lives.
Signs are shaped by different cultures in different ways and come from two different sources. Natural semiotics, for example, is the idea that you put on warm clothes when it's cold outside. In contrasti, conventional semiotics is how you wear those warm clothes and how that contributes to your identity as an individual.
In every semiotic, there is a signifier and a signified. There can be a signifier with different signifieds and there can be different signifies with the same signified. Whew that's a mouth full. Let me draw this up for you.
Here's Adam and Eve, being rebellious and eating fruit they shouldn't be. In the painting it seems like they're eating apples, but the Bible never actually specifies what kind of fruit it was. Therefore, an apple can signify many different things depending on its context:
Apple = Apple, but it can also = Healthy or = Fruit
Apple = Apple but Apfel = Apple as well as Pomme = Apple
I also thought synedoches were interesting extensions of semiotics. The idea that you can use part of something to stand for an entire thing.
You want to put on some blue suede shoes now right? I think synedoches can have powerful design influences specifically within the realm of book jackets. They articulate an idea or identity simply and swiftly and resist getting caught up in the details. That's just the recipe for book covers, interesting, thought-provoking, but straight and to the point. Because after all, the reader needs to get past the book jacket in order to get in there are start turning some pages.