Here's what happens when airplanes go to higher altitudes.
First, there's less oxygen, so they have to have ways to get enough, like turbo-charging. Jet engines have built-in turbo-charging, and supersonic engines also use ram effect.
Second, since the air is less dense, they need to go faster to get the same lift. That's a good thing. It's why long-distance aircraft go as high as they do. But there's a problem. In colder air the speed of sound comes down, and if their airspeed approaches the speed of sound they can get into problems. This is called the "Q-corner" or "coffin-corner". To go faster than that they need to be designed for supersonic flight. So, for example, subsonic transports are limited to about 40k feet, while the supersonic Concorde cruised at 60k feet.
For human-powered flight, it's strictly a matter of having enough power to overcome drag. Niels is right about ground effect. When an aircraft is within one wing-length above the surface, drag is greatly reduced, so much less power is needed. If you take a flying lesson you learn to watch out for this, because you don't want your aircraft to "float along" when you're trying to get it on the ground. But it can help if you're taking off on a poor surface. You get into ground effect and stay there while you accelerate.