What does pO2 of blood mean and why do we use it?
There is a good explanation in Relating oxygen partial pressure,
saturation and content: the
haemoglobin–oxygen dissociation
curve Breathe 2015; 11: 194–201


  The partial pressure of oxygen (also known
  as the oxygen tension) is a concept which often
  causes confusion. In a mixture of gases, the
  total pressure is the sum of the contributions
  of each constituent, with the partial pressure of
  each individual gas representing the pressure
  which that gas would exert if it alone occupied
  the volume. In a liquid (such as blood), the partial
  pressure of a gas is equivalent to the partial
  pressure which would prevail in a gas phase in
  equilibrium with the liquid at the same temperature.
  With a mixture
  of gases in either the gas or
  liquid phase, the rate of diffusion of an individual
  gas is determined by the relevant gradient of its
  partial pressure, rather than by its concentration.
  While in a gas mixture, the partial pressure
  and concentration of each gas are directly proportional,
  with oxygen in blood the relationship
  is more complex because of its chemical combination
  with haemoglobin. This allows blood
  to carry an enormously greater concentration
  (content) of oxygen than, for example, water
  (or blood plasma). Measurement of $p_\ce{O_2}$, therefore,
  does not give direct information about the
  amount of oxygen carried by blood. 


So blood $p_\ce{O_2}$ does not correspond to a particular concentration of oxygen, because the concentration of haemoglobin can vary, and most of the oxygen is bound to the heme iron.  

$P_\ce{O_2}$ is the partial pressure of oxygen in a hypothetical gas phase which would make the blood oxygen and gas phase oxygen be in equilibrium.