By allowing a bottle of wine to be exposed to air the wine's tannins will soften, along with its acidity.
Opening a bottle and leaving it for 2-6 hours often helps cheap and expensive reds and whites that should be aged more to open up and taste better.
There are a number of ways of speeding up the breathing process:
Decanters which allow a large surface area of wine to mix with air speed up the process.
Aerators come in all sizes but usually look like a funnel with holes to spray the wines out the sides of the bottle.