There are four reasons why you want to decant a wine
Sediment - When wines age and even some young unfiltered wines have a lot of sediment so you would want to decant them before service. If time allows, have the bottle upright for a few hours, otherwise keep it on its side and use one of those lovely wine service carriers that keeps the bottle on an angle. When you decant these wines you pour the wine into the decanter with a candle lit below to illuminate your process. Once you see sediment coming, stop pouring, keeping the sediment in the bottle away from the wine you will be drinking. For older wines this is done slowly and just before drinking so to allow as much of the character to be in place.
Young Wines - Some young wines just need a spanking. This type of decanting is not done gently. You want to slosh it around so that it receives the maximum oxygen introduction.
Ambiance - There are lovely decanters that are on the market and can grace the table elegantly.
Hide ugly labels - We eat and drink with our eyes. Do need to say more?!