In a nutshell: decanting is pouring wine from its bottle into a pitcher, and “letting wine breathe” is exposing it to air. Decanting removes sediment, and aerating gets rid of certain odors.
Port and older red wines (10+ years), sometimes develop sediment, and benefit from decanting. Sediment, which comes from the wine’s tannins and pigment, is natural and won’t hurt you, but it doesn’t look or taste good either. Once it’s rid of sediment and displayed in a decanter, an older wine looks particularly elegant.
Sometimes a young or less expensive wine benefits from breathing. Aerating can help get rid of minor wine faults, such as gassiness. Merely opening the bottle does not provide enough air contact to improve the wine, but pouring wine into a decanter or glass lets it aerate more effectively.
Emile Peynaud, the highly respected author of The Taste of Wine/The Art and Science of Wine Appreciation, recommends decanting just before serving because “nothing happens physically or chemically in two to three hours.” Other experts suggest decanting ½ – 1 hour before serving. If you’re nervous about decanting in front of your guests, earlier preparation should be fine; it’s more important to do a good job.
A few days before serving or decanting a treasured wine, clean your decanter because it takes a long time for the inside to dry. Also, let the bottle sit quietly at room temperature for a few days so that the sediment settles to the bottom of the bottle.
When you decant, you should be able to see the wine and sediment flow through the bottle to its shoulder and neck, either by removing the capsule from the neck and/or placing a light (candle, flashlight or lamp) behind the shoulder and neck. Pour slowly and without stopping until the sediment is just about to escape.
Decanters usually hold one liter of liquid, so wine from a standard 750 ml bottle will easily fit inside and also leave air space. Decanters come in a large range of quality, styling, craftsmanship and price (over $1,000 to below $30) and are widely available. Some resources: Esque, Baccarat, Reidel, Villeroy & Bosch, Schott Zwiessel, Rosenthal, Ravenscroft, Williams Sonoma, West Elm, Pottery Barn.