Oxygen, or air, has a love/hate relationship with wine. In small amounts, particularly when a bottle is just opened, air is needed to help most wines open up allowing many aromas and flavors to emerge. That is the reason most wines will benefit from the use of an aerator or decanter. However, if a wine is overexposed to air it can become oxidized and basically spoiling the wine. Wine oxidation is fairly easy to recognize both in color and smell. White wines will turn to a gold or even brown color and will smell more like apple cider or sherry whereas reds will turn to a brick red or tawny brown color and can have a caramelized quality or vinegar scent to it. This can happen within a day of opening a bottle and just putting the cork back in the bottle and leaving it out on your kitchen counter... the air will work that fast in ruining a perfectly good bottle of wine!
By preserving the wine, you are basically protecting it from the harmful effects of oxygen. There are many ways this can be achieved and is covered in further detail in the section "Different Forms of Preservation"
, but one way or another the goal is to ensure the wine does not interact with any surrounding oxygen. This way you don't have to finish that stellar bottle you just opened all in one sitting and can enjoy it over the next few days or possibly weeks depending on what preservation method you utilize.