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.
