It is closer to being saturated with moisture at that temperature than otherwise. Therefore, to become completely saturated, the temperature would have to be decreased less. Thus, the dew point spread is lower. The closer the dew point is to actual temperature, the closer to saturation the air is. That makes sense.
When dew point spread is low, that means the air is nearly saturated with water vapor. You would not need to decrease the ambient temperature by much to put it into saturation. As such, when it is humid outside, the air is much closer to saturation than otherwise, and the dew point spread is low. That is the relationship you see when it is cloudy or foggy. The air has enough moisture at those temperatures to be visible, and it would not have to get much colder for it to drop from the