The plane is pressurized from the engines, and the cabin air is entirely replaced with new, fresh, outside pressurized air every few minutes.
There’s a bleed valve in the tail area where it blows out.
The recirculated air is filtered, so viruses and bacteria are not really a problem. What recirculation brings is better airflow and humidity.
On a plane, the outside air is incredibly cold and dry. The cold is not a problem: air is heated by the engines before it enters the cabin. Humidifying the air would be a problem however as it would require heavy humidifiers and water tanks.
The idea that 100% of the air is recirculated is obviously wrong, we would all die of hypoxia it it was.
Why do they do that? I leave mine of full blast the whole flight to stay cool.
Air comes in ducts, air goes out ducts. You get fresh air. Both the fresh fraction and the recycled fraction are HEPA filtered.
Edit: another comment here says the mean replacement time for air in an airliner is 4 to 5 minutes with a recirculating ratio of about 50%. I'm not sure if that's right, but it feels about right. Imagine your share of the space in the cabin. Think how long you could sit in a sealed cardboard box that size before the CO2 levels started making it feel stuffy. The airliners aren't carrying around hundreds or thousands of kg of lithium hydroxide to scrub the CO2. They're just dumping stale air overboard.