What does "no significant cytologic atypia mean"?

Hi James,
Breaking it down etymologically, "cytologic" basically means "of or relating to cells" and "atypia" means, well, "atypical."  In the setting of a nevus, this means that there wasn't a significant proportion of the cells that showed an abnormal appearance consistent with atypical growth, division of cells, or transition to a type of cell inconsistent with what was taken out (like finding gut cells in a skin mass, which is relatively rare).  If you cut out skin from a variety of people, there would likely be some cells that look atypical, but as long as the relative proportion of atypical cells is small, there's nothing to do but watch closely, as the body generally does a really good job of killing of cells that are trying to act up and divide without being told to do so.  Unfortunately, there's no such thing as a "100% guarantee" when it comes to the human body, but there being "no significant cytologic atypia" means that, per the guidelines of the pathologist, the nevus removed was benign.  

On online forum is not really the place for this question since I have no clue about your particular case - no photos, not what was done, nothing. That is why I anticipate few if any people will respond to your question. The proper place to discuss this is in detail with your doctor. That being said, and making the disclosure that this is NOT IN ANY WAY a comment about your particular case, in general, a "nevus with no significant cytologic atypia" means it is likely a benign condition. 
Good luck and review with your doctor.
Damon B. Chandler, MD
Harvard-Penn Trained Oculofacial Plastic Surgeon