Our cells have p53 proteins that serve many functions in preventing cancers. They settle cells down, they allow cells to repair when our natural DNA breaks down, and they help the DNA repair process. When HPV 16 E6 is around, the p53 proteins do not do their job. E7 proteins, E1 proteins and E5 proteins from various HPV types can all interact with natural tumor control mechanisms of other type to also cause a propensity to pre-cancer and cancer.
The HPV virus lives on skin, and sexual contact and touching spreads it. It's possible that some sex toys have been able to spread the HPV virus, but this is not how most people acquire their infection. The HPV virus grows in a fascinating way. It stays quiet, or comes alive and starts reproducing its shell first; when some of the most upper level, towards-the-surface epithelial cells (surface-type cells, but these can be anywhere like the cervix, the vagina, or the penis) start to mature, in a sudden spurt, the final steps that create the whole virus, the virus particles, are released. Because the quiet step can be so long, and so quiet, it is able to escape detection from the person's immune system and that's the reason not everyone clears their infection. In those that do not clear their infection, the pieces of the virus that can cause the various cancers of the genital tract can take hold.