An object with mass has a quality called inertia . If you shake an object like a stone in your hand, you would notice that it takes a push to get it moving, and another push to stop it again. If the stone is at rest, it wants to remain at rest. Once you've got it moving, it wants to stay moving. Mass is a measure of how much inertia an object displays.
Weight is an entirely different thing.
Every object in the universe with mass attracts every other object with mass. The amount of attraction depends on the size of the masses and how far apart they are. For everyday-sized objects, this gravitational pull is vanishingly small, but the pull between a very large object, like the Earth, and another object, like you, can be easily measured. Scales measure the force of attraction between you and the Earth. If you are in a spaceship far between the stars and you put a scale underneath you, the scale would read zero.