Solubility of Gas in Liquid

Hi, Could you explain me the below highlighted statements which i red from "http://www.amcresidents.com/Lectures/Dr_Trickey/Solubility.htm"
Solubility.Henry's law: (1803)At constant temperature, the amount of gas dissolved in a liquid is proportional to the partial pressure of the gas with which it is in equilibrium.Solubility also depends on the specific vapor and the specific solvent.With temperature and pressure, we need to define "amount" - as in Henry's law. Although the "amount" of gas (and its activity) are directlyproportional to pressure, this refers to the number of molecules; the higher the pressure, the greater the number of molecules, but they are compressed(Boyle's law). Volume is a function only of temperature.If temperature is not constant, the amount of gas or vapor dissolved is inversely proportional to the temperature.

Ostwald solubility coefficient.

Volume of gas dissolved in unit volume at ambient temperature and pressure. In anesthetic practice, these are quoted in tables, assuming a body temperature of 37°C. Note that the volume of gas dissolved is only dependent on temperature, and not pressure (though the number of molecules and the activity of these is pressure-dependent).

Thank you