Mole removal came back abnormal

I recently had a mole removed because my dermatologist wasn't happy with the way the mole looked and had been changing.  When they sent it away to be checked it came back with abnormal cells.  Their response to me was to stay out of the sun as often as possible (wearing SPF 30-45) and getting a check-up once a year.  
My question is should I be concerned that the cells were abnormal?  Could this lead to melanoma? Should I be concerned that it could have spread before removal? Is there anything I can do to see if the abnormal cells have spread elsewhere?