The structure or body of a wine refers to its “weight”. The simplest way to understand is with the soup metaphor: where the weight ranges from broth, the least…to hearty stew, the most.
If you haven’t opened a bottle and want to estimate the weight of the wine, you can look at the percentage of alcohol: 10-12% is low; 12.5-13.5% is medium; and 14-15.5% is high. (Fermentation stops at 16% so wines above that level are liquoroso meaning additional alcohol has been added.)
The level of alcohol is a good estimate for weight because in a well-balanced wine, the “softness” of the alcohol will counter the “hardness” of tannins, acidity and minerality. Since most of the structure of wine comes from tannins and acidity, the more tannic and acidic (ie. structured) a wine is, the more alcohol it will have to be in equilibrium. (NB. Using the level of alcohol as a proxy for structure assumes that the wine is well-balanced.)
If you have opened the bottle, there are several ways to sense the structure. First, you can look at the color of the wine. Often, a lighter, more transparent color means a lighter wine, but this is not always the case. Nebbiolo wines, for example, Barolo, Barbaresco, Nebbiolo, are lightly colored but very structured.
Another method is to swish the wine gently in your glass and look at the “legs” or “arcs” that form. The wider they are and the faster they fall, the lighter the wine is. Heavier, denser wine will have tight arcs and slide down the glass slower.
The last method is tasting. A structured wine will taste “heavier” in your mouth. The structure mostly comes naturally from tannins and acidity, but aging in wood barrels (particularly small barriques) also adds weight.
Structured wine will always taste best if it is paired with structured (ie. heavier) food. That’s why even a well-aged Barolo or Sagrantino di Montefalco pairs so well with red meat or game or aged cheese.