Before wines were routinely fined and filtered to a crystal clear state, it was quite common for wines poured from a bottle to contain a considerable degree of solid matter. In order to avoid bringing an unsightly looking wine to the table, it was quite the norm to decant the wine into a clear receptacle. The need for such a receptacle led to the development of the varied decanters available today.
Most wines today, have no real need for decanting to the same degree as was required in the past. The modern winemaking process ensures that wine is thoroughly clarified before it is bottled, by a process of fining (passing egg whites, Bentonite clay or other substances through to fine and collect solid matter) and mechanical filtration. Although these wines are often best served from the bottle (after all, you've paid for a finished wine), many benefit from decanting.
Wines which have aged in the bottle, typically red wines, will generally throw sediment by ten years of age. Not only is this sediment displeasing to the eye, it can also be quite unpleasant on the palate. These are the wines that deserve decanting, (giving wine respect).
Young wines also benefit from decanting, although the aim is not to take the wine off its sediment (there is rarely sediment in young wines), but rather to aerate the wine.
The action of decanting, the surface area in contact with the air in the decanter, alters the wine, softening its youthful bite, astringency and acidity, encouraging the development of more complex aromas that normally develop with years in the bottle.
For this reason, even inexpensive wines can benefit from decanting, if a first taste reveals a tannic, grippy, astringent structure, but good fruit in the background.
Having confidence in the wine and giving it time to breathe will bring back the harmony of all these unique and exciting components, layers and flavours in the wine and bring them into balance to your taste buds.