John Smith gave you the correct answer: the absolute humidity decreases with altitude. Here is an example:
A cubic meter of moisture saturated air at 15 degrees Celsius cannot contain more than 13 grams of water. If that air rises and cools down by the average adiabatic lapse rate of 0.65 C per 100 meters, when reaching 2,300 meters, the temperature will be 0 C (freezing point).
But at that temperature, the air is already saturated with only 5 grams per cubic meter. It means that, during that rising, the air must get rid of 13 - 5 = 8 grams of water per cubic meter.
... and it does it by condensation and that's how clouds are forming! :-)
So, the absolute humidity (volume of water per volume of air) decreases with the altitude but the relative humidity (percent of saturation point) stays the same in both cases since the air is still saturated and the relative humidity is 100 percent.
But if we had done the opposite operation and warmed up a saturated air parcel from 0 to 15 C, the relative humidity would then have dropped to 5 / 13 * 100 = 38 percent and that is relatively dry air.
And this explains why, during the winter when you get the outside air warmed up inside you home, the relative humidity is very low and, why when you fly an airliner at 30,000 feet above sea level, the air feels very dry.