Cervical cancer is caused by the human papilloma virus (HPV). However, there are many many types of HPV, some which cause cervical cancer, and some that don't. Some we can test for, and some we can't.
HPV is considered an STD, because there really is no other way to get it; HPV is transmitted from person to person via sexual activity. This HPV also interacts with certain factors - like your genetic predisposition, before cancer actually happens. Our immune system has cancer-fighting cells, that actually work pretty well for the most part.
Cervical cancer is NOT caused by other STD's like chlamydia, syphilis, etc. However, if you have HIV/AIDS, it can "encourage" a current HPV infection to create cervical cancer as well.
There is ONE other known cause of cervical cancer unrelated to HPV, and that's a drug called DES (shortened form). If your mother took this, it can cause you to get cervical cancer.
If you've had one session of genital contact, that is, unfortunately, how you probably got HPV, followed by the cervical cell change noted on your PAP smear. However, your cervical cells, even if they change, can go back to normal as well - so you won't necessarily get cervical cancer from this.