Relative humidity is often used to describe the amount of water in the air. It describes the difference between the actual water content of the air in evaporated form (as gas), and what maximum the air can actually hold. In other words, if the relative humidity is 50%, it means that the air only holds 50% of what it actually can hold.
The amount of water that the air can hold depends on temperature. When the temperature increases, air can hold more water in evaporated form. This means that if the temperature increases, the relative humidity autmatically decreases assuming that the water content of the air remains constant.
The drying capacity of air depends on relative humidity. Drying occurs if there is a driving force towards the air. If the relative humidty is low, air can take up a lot of moisture before it becomes saturated. This will create a larger driving force (more drying) than when the relative humidity is high. Because relative humidity goes down with an increase in temperature, warming the air is effective for increasing the drying capacity.
When there is actually more water in the air than the air can hold, it can not evaporate anymore, and it will form a mist. This means that when temperature drops, the relative humidity goes up (because the air can take up less moisture) until the level of 100% is reached. This temperature is called the dew point. If the temperature drops more, below the dew point, fog or condensation will occur.
The same happens when a cold object is placed in a warm environment. The air immediately surrounding the object will drop in temperature, and the relative humidity at the surface will go up. If the temperature of the object is at or below the dew point, condensation will occur.