How does the temperature of the air influence it's ability to hold water vapor?
The equilibrium vapor pressure of water in the atmosphere is the point at which evaporation equals condensation so there will be no net evaporation of water into the atmosphere. This can be thought of as the maximum amount of water that the atmosphere can hold. The equilibrium vapor pressure of water increases with temperature, thus more water can evaporate into the atmosphere as the temperature increases.
The measure of water vapor in the atmosphere is called relative humidity. Relative humidity is defined as the ratio of the partial pressure of water vapor in the atmosphere to the equilibrium vapor pressure at that temperature. One way to look at relative humidity is that it's the ratio of how much water is in the atmosphere to how much water can be in the atmosphere. When relative humidity equals 100% the atmosphere is saturated with water vapor and water will begin to condense.
When the temperature increases the relative humidity drops because the equilibrium vapor pressure has increased. The atmosphere is now at a lower percentage of saturation so water can continue to evaporate.
When the temperature drops the equilibrium vapor pressure decreases so the relative humidity increases. If it increases to 100% water vapor will begin to condense. The dew point is the temperature at which this happens.