Cigars are fine natural products, breathing through their wrapper. Even after years they do not lose their unique features, granted they are stored right. A perfectly stored cigar has a soft shine to it, is gentle and give in to the most delicate pressure. Especially heat, direct sunlight and smells are to be kept away from the cigar (never keep a cigar in the fridge). The best way to store cigars is in a so called Humidor, a box maintaining a relative humidity level of 65 - 70 percent and a temperature of approximately 20 degrees celsius.
Make sure to ventilate your Humidor regularly and only use destilled water for the integrated humidifying system, since tap water can cause mould to grow. In case of mould infestation the cigar has to be removed. However, don't confuse mould with a white-grey fluff that can appear because of ongoing fermentation inside the Humidor. This fluff can be removed with a soft cloth.