They come from certain strains of HPV. Most sexually active people will have hpv in their lifetimes but the body cures it on its own. Sadly, there are certain types of hpv that can cause cervical cancer or genItal warts. There is no cure, but the warts can be removed by a doctor thru cryotherapy (freezing them off) or other methods. They can still come back once removed, but probability is low.
This is a good explanation - http://www.cdc.gov/std/treatment/2010/genital-warts.htm.