Weightlessness condition inside an orbiting satellite

Weight of a body is the force with which the body is attracted by the earth towards its centre.

When a person is standing on a surface, he presses the surface downwards with his weight in action. The surface exerts a reactional force on the person equal and opposite to the weight of the person. That is why he feels his weight.

When an astronaut of mass m in a satellite is orbiting around the earth, then satellite and every object inside the satellite has an acceleration equal to the acceleration due to gravity directed towards the centre of the earth. So astronaut is unable to exert weight on the floor of the satellite, in turn satellite does not provide normal reaction on the astronaut. Therefore, the astronaut feels weightlessness.

Weightlessness does not mean the absence of gravity, it simply means a situation by which an astronaut feels that he is not attracted by any gravitational force.