A much used, but rarely defined (clearly explained) wine term. A wines balance refers to how it handles the key components of alcohol, tannin, acidity, residual sugar, varietal typicity and winemaking techniques. They combine to display initial sensations on the senses and palate. Ideally these components will be idealy-balanced, and one will not be more prominent or lacking than the others.
Good balance is one of the most desired traits in a quality wine; balanced wines are symmetrical and tend to age gracefully. Balance is a concept that on the surface seems very simple, but is quite challenging. By far the most straightforward balance is that between sugar and acidity. Not all wines, of course, have residual sugar, though all have some acidity.

 

In its simplest sense, a wine which has a good acid-sugar balance, tastes neither too sweet nor too acidic: both exist in the right quantity. A wine with too little sugar for its acidity will taste harsh, sharp and acidic; the evolution of flavours in the mouth will be interrupted by the sensation of acidity. A wine with too little acidity and too much sugar, will taste cloying and flabby and out of balance on the palate and finish.

The balance between astringency, tannins and acidity in red wines is of paramount importance. The less tannic a wine is the more acidity it can support, if a red wine is high in tannins, the lower its acidity should/can be. Another important balance is that between alcohol and acidity / astringency. This is obviously most relevant to red wines. Too little alcohol will cause the acidity and astringency to dominate, making the wine taste harsh and thin. Too little acid and astringency will cause a wine to taste overly soft, heavy and flabby.
Other aspects of wine which exist in balance are oak vs. fruit and age vs. youth. As you can imagine these are almost entirely in the realm of subjective response; some wine enthusiasts love oaky wines, while others would call the same wine unbalanced. The temperature at which a wine is served can also have a dramatic effect on the balance of its various elements, plus a wine's balance may only be realized after some time aging - enjoy the journey.