At its simplest a dry wine is one with practically no sugar. Dryness is the absence of sugar; not a property in its own right. I would call that the technical definition of a dry wine, and it is the one I prefer to use.
But do you remember what I said in my last blog post about acidity and sweetness counteracting the effects of each other? When many people place a wine on the spectrum of dry to sweet, they do so on the basis of the perception of dryness or sweetness rather than the actual sugar content. Thus, a wine with a little sugar but high acidity will be classified as dry. Conversely, if a wine has aromas of ripe fruit it may also be perceived to be a little sweet, even if it contains very little sugar, and such wines might be classified as off dry.
When large wine merchants (including supermarkets) describe wine by a number on a scale from dry to sweet, I believe it is this perceptual sweetness they are describing. And they are in good company – even EU regulations allow a wine labelled “dry” to contain more sugar if is it high in acidity. While designed to be helpful, I find it confusing, which is one reason why I prefer the simple technical definition of dryness. The other reason is that sweetness and acidity are to me clearly different dimensions, even if there may be some perceptual interaction.
In many cases, the distinction between technical and perceptual dryness is not important, but if you ever feel there is a possibility that some confusion might arise it is best to specify exactly what you mean.
You should also be aware that there are a couple of other ways in which dry is sometimes used/misused…
One is in marketing. The fashion now is to drink dry wines, and one result of this is that many people say they prefer dry wine because it sounds more sophisticated, even if they actually prefer their wines to be off dry. This results in wines, usually at the cheaper end of the market, being sold as dry when in fact they contain noticeable sugar.
The other is when people encounter a highly astringent wine, and describe it as dry because the effect of astringency is to give you the impression of having a dry mouth. The use of the word dry in this context is understandable, but likely to cause confusion if you are communicating with someone who has been taught to distinguish between lack of sugar and astringency. This is one situation where you might hope that a good wine professional will be able to figure out what is really meant, but I wouldn’t count on it.