I can pull my gum away from my teeth like a flap...what does mean?

Not sure what you mean exactly without a pic but assuming you have NOT recently had a survey,  this could be a sign of a genetic anomaly to a serious disease condition. See a periodontist to assess. 

Healthy gums tend to form a tight collar around your teeth.  Were your gums very firm at one point and now are loose?  Definitely go and see your dentist and have them check for periodontal disease.  They will measure the spaces around your teeth to see if they are deeper than normal.  They will also check for areas that bleed when probed.  Some people however have excess tissues and this may be the case with you.  It can give the appearance of short teeth and in addition maintenance can be a challenge as you have to get well below the gum line on a consistent basis.