GSM is Grams per Square Metre. It is basically the weight of the paper or paper density. In most parts of the world people use the term grammage instead of GSM. You can get different paper density...just depends on what you would like. The thicker the paper (high GSM number) the higher the quality. I hope this helps.
GSM is Grams per Square Metre as state above, however "The thicker the paper (high GSM number) the higher the quality" this totally inaccurate, thickness is measured in Microns (one thousandth of a millimetre) not GSM.
The quality of paper is another thing all together and has nothing to do with GSM or Microns.
I never really understood why people in our industry use these terms. Why "gsm" instead of g/m2,gm-2 which I believe would be the right SI units? Don't even start me on 'grammage'! ;-) I guess it's just historic and cultural but I'd have had a proper roasting from my Physics teacher for using units like that.
GSM means paper density i.e. how many g a square metre of paper would weigh.