Something hit me during my last flight: our ears feel that the pressure around us changes quickly during liftoff and landing, they hurt more and more until we make them pop. However, the cabin must maintain a level of oxygen higher than outside the aircraft because it isn't dense enough at ~10km to breathe normally.
Does that mean that the aircraft merely takes air from the outside, heats it up (it's around -40°C outside at 10km) and adds oxygen to it before blowing it inside? How else?
Because the cabin isn't pressurized to sea level pressure instead it to about 8k ft equivalent. (while the plane is 4.5 times higher)
This means there is less differential pressure than if the cabin was pressurized to sea level pressure. But it's still within the limit of what passengers feel comfortable with.
This answer on aviation.SE contains a plot of cabin pressure over time during a flight:
The composition of air doesn't change with altitude just the pressure. This means that you only need to compress the air before blowing it in.
There's a difference between being pressurized to an absolute value and being pressurized to a relative value.
For instance, if the cabin immediately pressurized to the same atmospheric pressure as your departure terminal, then your ears would not pop on ascent, but they would have to pop at some point on the descent unless the elevation of the landing terminal were the same as the departure.
This would also mean that the aircraft structure would have to be thick enough to withstand the full differential pressure between up to sea level and cruising altitude.
If instead the cabin only pressurized to, say, 7psi (about 50kPa?) above whatever the outside pressure is, then there's no need for an elaborate destination pressure matching scheme and the aircraft walls can be made thinner, thus lighter and more fuel efficient.
Relative pressurization means the absolute pressure changes with altitude, so your ears pop.
