Mass is the measure of an object's inertia—how difficult it is to accelerate. The harder an object is to shake, the more mass it has. In contrast, weight is the force that gravity exerts on an object. The harder an object is to lift, the more weight it has.
To understand the difference between these two quantities, imagine a sealed box that rolls easily on wheels along a smooth, level surface. You can't see inside the box, so you have to conduct experiments to figure out what it contains. If you want to know how much the box weighs, you simply pick it up. To keep it from falling, you'll have to push upward on it with a force that exactly balances its downward weight. The more the box weighs, the harder you'll have to push upward.
But to determine the box's mass, you don't pick it up at all. Instead, you roll the box back and forth. The more mass the box has, the harder it will be to start and stop this rolling. Weight has nothing to do with this process—the wheels are supporting the box's weight. You're simply determining how hard it is to shake the box and thus how much mass it has.
Fortunately, mass and weight are related. It's a remarkable fact that in a given location, an object's weight is exactly proportional to its mass. Thus a 2-kilogram box of sugar not only has twice the mass of a 1-kilogram box, it also weighs exactly twice as much. We're so used to this simple relationship between mass and weight that we use mass units such as kilograms and weight units such as pounds almost interchangeably.
Since mass has nothing to do with gravity, an object's mass doesn't vary from place to place. If the box is hard to shake on the earth, it will still be hard to shake on the moon, on Jupiter, or even in the depths of empty space somewhere. But the box's weight will vary with location because gravity varies with location. As I'm fond of telling my students, if you open an interstellar gourmet food business, you'd better label your products in terms of mass because if you label them in terms of weight, you'll be in danger of selling underweight goods on any low-gravity planets.
Finally, you remarked that in orbit, you have no weight. That's not exactly true. Actually, an astronaut in orbit around the earth weighs almost as much as on the earth's surface. But because the astronaut is freely falling along with her spaceship, she doesn't need any forces to support her and can't sense her weight. To truly get rid of weight, you'd have to go infinitely far away from anything else in the universe or find a place between stars and planets where all the forces of gravity cancel perfectly.
Answered by Louis A. Bloomfield of the University of Virginia