Why does a glass of water left out in air vaporize (eventually) even though it's not at boiling temperature?

According to my book:

“If the air is sufficiently dry and the water vapor is allowed to move away from the glass once it escapes from the liquid, the vapor pressure of the water will always be greater than the partial pressure of the air due to water. So water vapor will continue to slowly escape from the water until water is gone.”

Can some explain it in simpler terms so I can understand it XD?