Phil Plait explains the physics behind this very cool video:
They filmed this video on an airplane capable of making steep arcs up and down in the air, over and over again. Near the top of the arc, the only forces acting on the plane are gravity and air resistance. The engines are cut back and the plane pitched to an angle that exactly compensates for air resistance, leaving only gravity acting on the plane…
During those brief seconds around the top of the arc, the plane and all the objects inside it are freely accelerated* by gravity at the same rate, so to anyone inside, they feel weightless! If you hold up a ball in front of you and let go, it’ll appear to float there. Really you’re just all traveling along the same ballistic trajectory, but your body will feel like it’s freely falling.
And that’s the trick to this video! They built a mock airplane cabin inside of a Russian Ilyushin-76 airplane (flown by the Russian S7 airlines), and filmed it as the plane made a series of arcs. So when you see them floating around weightless, well, that’s no trick. Except a trick of … SCIENCE.