Mommy4 is right. Atypical means cellular changes, which is why your doctor wants to monitor you. Here are some links that migh help explain this for you. Some of them are older, but the info is still helpful.
http://www.mjbovo.com/Women/AbnlPap.htm
http://www.womenshealth.org/a/atypical_cells_pap_smear_resul
http://www.gynalternatives.com/cervical_dysplasia.htm#ASCUS
I definitely understand your concern about it turning into CIN II or III, again, though. I'm glad you got your lab reports. But has your doctor explained any of this to you or given you any information to read? In addition, have you had the HPV DNA test done, yet, to find out what strain(s) you have? There is currently Digene's test. But Roche also has a new HPV DNA test, too, which I have been told is even more accurate. I had that done. It's just harder to get ahold of the new test because insurance companies may not want to pay for it. You may have to ask for it, and if your doctor doesn't have it, check a teaching hospital about it. If you can find out what strain(s) you have, it could definitely help your doctor and you decide how to address this. It made all the difference for me. In addition, if you're not comfortable with the answers you're getting from your doctor or if you don't feel you're being given all the information you need, please don't hesitate to get a new one. In any case, a second opinion always helps.