Due to the reduction in air density by gaining altitude, lower air pressure or higher ambient temperatures an aircraft engine loses some of its rated power. At about 10000 ft the air pressure has dropped about 25% compared to sea level. Thus the engine gets 25% less air per intake stroke and therefore is reduced in power output. As a results aircraft performance suffers in climb ratio's, cruise speed and more. Even the pilot in an unpressurized cabin suffers and must be using extra oxygen when staying longer than thirty minutes above 10000 ft.
In the pdf file below you wil find more detailed information from AMT (1997, dated but still current).
Excerpt from the document:
Turbocharging an aircraft engine is analogous to a mountain climber making the demanding ascent of Mount Everest aided by supplemental oxygen. Without such help, each advancing step becomes slower and more difficult. Oxygen deprivation slowly saps the strength as every breath of air becomes more labored than the last. A satisfying gulp of bottled oxygen quickly renews the energy required to gain higher ground.
It is the same with a naturally aspirated engine. As a pilot nurses his plane toward its service ceiling, performance diminishes noticeably.
To continue reading see the pdf below: