The body of a wine has to do with weight, or how it weighs on your palate. The best way to understand this would be to take four glasses, filling the first with water, the second with skim milk, the third with whole milk, and the fourth with cream. Take the water in your mouth and feel it. It feels light and, of course, watery. The skim milk will feel a bit more weighty, but still light, while the whole milk will start to feel more full. The cream will be the heaviest, with a full palate feel. You can go further with either heavy whipping cream or olive oil, but I think we should get the point. These go on a light to heavy scale just like wine!
Body can be judged in both white and red wines, still and sparkling, sweet and dry. White wine varietals which typically feel more like water or skim milk could include Sauvignon Blanc or Pinot Grigio, with reds being Gamay or Pinot Noir. Fuller bodied varietals tend to be more weighty like whole milk or cream. Full white varietals can be Chardonnay or Viognier, while reds can include Shiraz/Syrah or Cabernet Sauvignon.
Contributing factors for body are numerous. Not only does the varietal's natural juice count toward the weight, but so does it's vinification. Stainless steel fermentation, oak aging, maceration, malolactic fermentation, chaptalization, etc. can all affect the end product. Getting to know your varietals will help you determine what body each are, as most varietals tend to be around medium body, but can be lighter or fuller medium, depending upon where they are grown and the winemaker.
Getting to know about the varietals will also help you determine what you'd like to drink. If I am outside on a warm summer day eating some oysters, I might pick a Muscadet, made from the Melon de Bourgogone varietal, which is lighter, with a touch of salinity. If it is a bit cooler out, and I am eating some cumin spiced pork chops, I may go for a Sonoma Zinfandel, for its rich weight and slight sweetness and spice. If you have any trouble finding a good pairing, ask the Windy City Wine Guy!
(photo courtesy of flickr)