The word "Aesthetics" comes from a Greek root meaning "having to do with the senses." It started out in philosophy, having been invented by the 18th century German philosopher Alexander Baumgarten to describe the philosophical study of what can be perceived by the senses. You can see the same root at work in some more every day words like "anaesthesia", which literally means "without feeling", or in the less common "synaesthesia", which means "combining several senses" (as one might do with a light show at a rock concert, or a multimedia show).
"Aesthetic" has some related technical senses that we will use in this class.
1) An "aesthetic" is an artist's or even a culture's sensibility, how the artist (to use the simpler case) approaches his or her work, what he or she is trying to acheive. So you can talk about Cezanne's aesthetic, about David Milch's aesthetic, or for that matter, about an "aesthetic of the everyday" that is often said to characterize traditional Japan. Some of you are painters or dancers or musicians; as you develop, you are finding and growing into your personal aesthetic--in other words, your vision and voice, the approach to work that seems right for you.
2a) Aesthetic considerations can be considerations related to an object's appearance, how it pleases or otherwise strikes the senses.
2b) Aesthetic considerations can be considerations related to something's being art. This use, as we'll see, is very slippery--be careful with it!.
3) The word "Aesthetics" is often used to mean "the philosophy of the arts." That's what it means in the title of this class. I'm getting ready to change the title of the course soon, to Philosophy of the Arts, because this usage is not universal, and it can be confusing. Some artists (e.g. Marcel Duchamp, Barnett Newman, Sol Lewitt) and some philosophers (e.g., Arthur Danto) use "aesthetics" exclusively in sense 2a above, and make the point that art is not about aesthetics, or at any rate that it doesn't have to be.
Here is a link to an article in the Routledge Encyclopedia of Philosophy about Aesthetics, by the contemporary philosopher of music Malcolm Budd: