Dalton's Law = The pressure of a mixture of gases is the sum of the partial pressures of the constituent gases.

In terms of the composition of air, (78% N, 21% O2, 1% other, ie "a mixture of gases"), this means 21% of atmospheric pressure is due to O2.

Although these percentages are constant with increasing height, the amount of 'inhalable' O2 reduces due to decreasing pressure - this is essentially what 'Partial Pressure' (PP) means, eg:

PP of O2 at MSL = 21% x 1013 = 213mb

PP of O2 at 30,000ft = 21% x 300 = 63mb

Human body very susceptible to reductions in PP of O2 - anything below 55mm/Hg will induce Hypoxia, ie reduced air pressure resulting in less O2 being pushed through the veins. Above 38,000ft, O2 needs to be administered under pressure.