The temperature at which air becomes saturated with water vapor is known as the dew point temperature. The dew point is the temperature at which the air is holding the maximum amount of moisture it can at a given pressure, leading to saturation and potential condensation of water vapor into liquid water (dew) or forming fog.

The amount of water vapor that air can hold does indeed increase with temperature. Warmer air has a higher capacity to hold moisture than cooler air. When air becomes saturated at the dew point temperature, it means that the air is holding all the water vapor it can at that particular temperature. If the temperature were to decrease from that point, the air would become supersaturated, and excess water vapor would start to condense into liquid water droplets.

In practical terms, when warm air cools down, it can reach its dew point temperature, and further cooling would lead to condensation. This phenomenon is why dew forms on grass and other surfaces during cool nights. When air containing water vapor comes into contact with a cooler surface, it can cool down to its dew point temperature, causing the water vapor to condense into liquid water droplets.

So, in summary, the dew point temperature is the temperature at which air becomes saturated with water vapor, and the amount of water vapor air can hold does increase with temperature.

Dr Gaurav H Tandon thank you for your contribution to the discussion

Air can become saturated due to evaporation, the mixing of two unsaturated air masses or by cooling the air. Water vapor in the atmosphere condenses when it becomes saturated and bumps into condensation nuclei. Nuclei are particles. Water vapor and liquid water can condense onto these nuclei. It will eventually reach point C on the saturation line, where the maximum moisture it can hold is 0.010 08 kg/kg (approximately 14.2°C). It cannot be cooled below this temperature and still hold this proportion of water vapour, so moisture will be precipitated as dew. The Dew Point is the temperature at which water vapor starts to condense out of the air, the temperature at which air becomes completely saturated. As it cools, the air's capacity for water vapor (its saturation mixing ratio) decreases. If the air cools to its dew point temperature (in other words if it reaches saturation with respect to water vapor), condensation is forced and some of the water vapor in the air condenses into liquid water droplets. If the air is moist enough, the cooling causes it to reach saturation and visible water droplets form. We often call this type of fog ground fog because it lies so close to the surface. Advection fog forms when warm moist air moves over a colder surface. The dew point is the temperature to which air must be cooled to become saturated without changing the pressure. Changing the pressure affects the vapor pressure and therefore the temperature at which saturation occurs. Thus, the dew point temperature is determined by keeping the pressure fixed. For a pure substance there is a definite relationship between saturation pressure and saturation temperature. The higher the pressure, the higher the saturation temperature. The graphical representation of this relationship between temperature and pressure at saturated conditions is vapor pressure curve. The higher the temperature of a solvent, the higher its saturation point. This is because a higher temperature of a solvent means that the molecules are moving faster and are therefore able to collide with more solute particles, resulting in more particles dissolving. When air holds as much water vapor as it can for a given temperature (100% relative humidity), it is said to be saturated. If saturated air is warmed, it can hold more water (relative humidity drops), which is why warm air is used to dry objects--it absorbs moisture. There is a common sense way. If you increase the temperature, you are increasing the average energy of the particles present. That means that more of them are likely to have enough energy to escape from the surface of the liquid. That will tend to increase the saturated vapour pressure. The saturation vapour pressure of water increases with increasing temperature and can be determined with the Clausius–Clapeyron relation. The boiling point of water is the temperature at which the saturated vapour pressure equals the ambient pressure.