TL;DR:

Facial skin is not only exposed more often to sunlight and as such more susceptible to the aging effects of UV radiation, but it is also typically much more sensitive to hormonal changes in the body, which you start seeing when you hit puberty in your teenage years. The extent to which it is sensitive to androgens depends mostly on genetics, and most of our skin problems resulting from androgen sensitivity relate to problems with the sebum (oil) the skin produces through tiny glands tied to each pore. For genetic as well as anatomical reasons, these problems more often occur on the face -- the chin, the forehead, and the back have the highest number of sebum glands per square inch, but because the face is more visible than the back and we tend to cover our backs in clothing, as well as once again for genetic reasons, sebum production is not typically as noticeable on the back as it is on the face. When the skin overproduces sebum, it creates oily skin, which not only attracts dirt, but also promotes the development of P. acnes, the species of bacterium responsible for acne vulgaris. The underproduction of sebum results in dry skin and its associated skin disorders. Androgen sensitivity and the rate of androgen production are why some of us go through our teenage years without developing acne at all, while others (myself included) still have very oily skin at the age of 25. When factoring in UV exposure and repeated muscle movements we use to create expressions, as well as the fact that the thinnest skin on our bodies is under the eyes and around the eyelids, our faces are much more susceptible to fine lines and wrinkles than most other areas of the skin.

Of course, there's also the fact that in our culture, we place a high priority on our facial skin looking great as it is how we physically present ourselves and a great percentage of our emotions to others, so we tend to desire to take care of the skin on our faces moreso than we do many other areas of our bodies. Hence, companies in the business of cosmetics can produce specialty products targeting our faces and the bags under our eyes and be absolutely certain people will buy them over other products that don't explicitly mention the face as its intended application site.