This is talking about how to dress, or wear your clothes. "layering" is a way to dress or wear your clothes to deal with the ever-changing weather. For example, you may wear a pair of jeans with a tank top. Then on top of that you would "layer"(add on top of that) a short-sleeved shirt or blouse, and then maybe a pullover sweater/jumper if it was very cold or cool. That way, if the day suddenly gets warmer, you can take off one or more "layers"(levels of) of clothing to stay cool. "the art of layering"- "the art of xx" is a fancy or formal-sounding addition. Other examples: I just bought a new stove, so now I can master the art of cooking. (instead of) I just bought a stove, so now I can learn how to cook. The first sentence just sounds a bit nicer. I hope this helps =O)

"Layering" means wearing many thin garments instead of one thick one, so that you can adjust to varying temperatures by putting on or taking off layers. "Art" here could be a synonym for "skill" or "technique." However, layering can also be decorative; some people intentionally dress in layers designed to produce a pretty effect, so the writer could also be suggesting that layering can be attractive as well as practical.