Mass is a measurement of your bulk. Most people call this "weight", but weight is actually the effect of gravity on an object's bulk. For instance, something on earth will "weigh" less on the moon, but "weigh" more on Saturn. However, the "mass" of the object on all three will be the same (unless you gain/loose mass due to eating changes while traveling between them).
In science, mass is measured in grams (premature babies are often measured in grams because they are a smaller measurement, so it is easier to see the change in mass). Most of us just measure our mass in pounds (the British actually use "stones" to measure mass!).
Just keep in mind that when people talk about "weight", they usually mean "mass". Science teachers are usually very picky about this difference, so if you are in science class use the word "mass", not "weight".