partial pressure
The air around you is a mixture — mostly nitrogen, with oxygen, a little argon and a trace of carbon dioxide. Imagine quietly removing every gas except the oxygen, leaving it alone in the same room. The pressure it would push with on its own is its partial pressure: the share of the total pressure that one gas in a mixture contributes.
Because in an ideal mixture each gas behaves as if the others were not there, a gas's partial pressure is just the total pressure multiplied by its mole fraction — its share of the molecules. The partial pressures of all the gases add up to the total pressure the mixture exerts.
Partial pressure matters because it, not the total pressure, drives a gas's chemistry and its movement. Oxygen crosses from your lungs into your blood because of its partial pressure gradient, and the partial pressures of reacting gases — not the total — are what set the position of a gas-phase chemical equilibrium.
At sea level oxygen makes up about a fifth of the air, so its partial pressure is about a fifth of atmospheric pressure — climb a tall mountain and that partial pressure drops, which is why thin air leaves you breathless.
Oxygen's partial pressure, not the total, is what your lungs care about.
Partial pressure is the per-gas idea; Dalton's law is the statement that the partial pressures add up to the total. The two go hand in hand but are not the same thing.