The simplest answer to this question is--an absence of sugar. Dry is the opposite of sweet. A wine cannot be dry and sweet at the same time. If you ask for something that is "not too dry" you are asking for a wine that is a little sweet. If you ask for a wine that isn't dry and isn't sweet you are being a tad confusing.
You will also hear the term "off dry" which means the wine is a little bit but not super sweet. Other terms you may see are "medium sweet" or "sweet." When you get to this point the grams per liter is a better way to sort out what is bone dry and what is super duper sweet. Wine Folly has a neat breakdown of how much sugar (in grams per liter) to give you an idea how much sugar is in a bone dry versus a super sweet wine. You can check it out HERE.
People can (understandably) get confused when tasting a fruit forward wine. Sometimes such wine will give the impression of sweetness without much sugar being present. Likewise a dry wine doesn't always mean there is NO residual sugar. Grapes, indeed, have some sugars in them that are not fermentable and these remain in a wine.
Here is a little, oft unspoken, wine secret; wine is created when yeast eats the sugar in grapes and poops (for lack of a better term) alcohol. In dry wines the yeast eats most of the fermentable sugars (fructose and glucose). In sweeter wines less pooping means more sugar in the wine. NOW...there are also fortified wines which is another matter. Discussion of Port, Madeira and Sherry can take place another time! Likewise for sparkling wines.
We will get into each of these later!