Mass is the property which reflects the quantity of matter within a sample. Mass usually is reported in grams (g) and kilograms (kg).
Mass may also be considered to be the property of matter that gives it a tendency to resist acceleration. The more mass an object has, the harder it is to accelerate it.
Mass vs. Weight
The weight of an object depends on its mass, but the two terms don't mean the same thing. Weight is the force exerted on mass by a gravitational field:
W = mg
where W is weight, m is mass, and g is acceleration due to gravity, which is about 9.8 m/s2 on Earth. So, weight is properly reported using units of kg·m/s2 or Newtons (N). However, since everything on Earth is subject to about the same gravity, we usually drop the "g" part of the equation and just report weight in the same units as mass. It's not correct, but it doesn't cause problems… until you leave Earth!
On other planets, gravity has a different value, so a mass on Earth, while having exactly the same mass on other planets, would have a different weight. A 68 kg person on Earth would weigh 26 kg on Mars and 159 kg on Jupiter.
People are used to hearing weight reported in the same units as mass, but you should realize mass and weight are not the same and don't actually have the same units.