The mass of an object is a measure of how much stuff it's made of. So it's
a property of the object, like the object's length or color. It doesn't depend on
where the object is located right now, or on what else is around it..
The weight of an object is the measure of the gravitational force between it
and something else. The strength of the force depends on the size of both
masses, and also on how far apart they are. So the weight does depend on
where the object is located right now, and on what else is around it.
I think that sums it up fairly well.