At a liquid-vapor interface, liquid molecules are constantly leaving the surface to enter the vapor phase, and vapor molecules are constantly adhering to the surface to return to the liquid phase. These two processes reach equilibrium when the “partial pressure” of the substance above the liquid is equal to the “vapor pressure” of the liquid at the temperature of the interface.
For example, when the partial pressure of water vapor in air exceeds the vapor pressure of liquid water, the water vapor will condense out of the air as dewdrops. This is also why sweating becomes ineffective for thermal management when the humidity is too high. A useful homework problem is to compute the partial pressures which correspond to “100% relative humidity” at a few temperatures, and compare to the vapor pressure curve for water.
Your source (which is screeenshotted but not linked) seems to confuse these terms. “Vapor pressure” is a property of a material. “Partial pressure” is a property of your environment. You can reduce the partial pressure of ethanol above a surface by replacing the air there with fresh, alcohol-free air from outside; the ethanol will then evaporate until the vapor above the surface is saturated.
The boiling temperature is where the vapor pressure becomes equal to the atmospheric pressure, so that liquid would still enter the vapor phase even if all of the pressure at the surface came from the vapor.