The Weight of something tells us how heavy it is, but the Mass is the amount of "stuff", or matter, and object has and this amount remains the same wherever the object is, even though it's weight will change depending upon gravity. This means even though our mass is the same - our weight varies depending on which planet we are stood on in the solar system! You can see how your weight changes using our Weight-Planet Calculator.
If you find the weight of something on Earth and then take it to the Moon and weigh it again, you will find that it is lighter when it is on the Moon. This is because the surface gravity is less on the Moon.
However, astronomers want to be able to say how much of something there is without having to worry about exactly where it is at the time. They therefore use the Mass of things.
The mass is the weight of an object on Earth divided by "g", the value of the surface gravity.