A box for storing cigars in optimal conditions (from Latin humidus meaning "moist", through French).

Cigars want to be kept at about 70° F, and a relative humidity of between 65% and 75%. This sort of moderately tropical microclimate is essential to cigar storage. Why ? Nothing much happens if it is colder than that, in fact you can even freeze your cigars. If it is hotter than that, though, certain insect eggs which may be present in the cigars will hatch. And those bugs will eat your cigars. If humidity is less than that, your cigars will become hard, possibly crack, and when you smoke them they will burn like tinder. Not pretty.
If it is more humid than 75%, the tobacco will probably swell, making for a "tighter" draw. If they get really humid, you may have evil fermentation phenomena.

Humidors are generally quite expensive. But you can build your own quite easily: use a tupperware-like thing (any brand will obviously do, as long as it has an air-tight seal). Store the cigars together with a humidifier: this can be built by soaking a little piece of sponge in a 50% water-propylene glycol solution. Too lazy for that ? Use a water-table salt slurry.
The humidifier, though, should NOT be soaked with pure water. This would tend to bringing relative humidity to 100%. The solutions indicated above have a vapor pressure or respectively 70% and 75%. The sponge should be kept in a perforated container: you can build one using a film canister.

If you don't smoke your cigar immediately, consider storing it short term in a cigar tube.