The Human Papilloma Virus is tiny by virus standards, less than 8000 paired pieces of DNA. There are many strains of this virus, and to be a strain, its DNA has to be almost pure; at least 7200 of the pairs have to be unique. The HPV Virus is unique because it's mighty although it's little. The tiny virus DNA can make some powerful proteins that can unlock a cell's control and cause it to grow out of control; in other words, cause it to be cancerous. The part of the virus that performs this is the E6 and the E7 region. HPV viruses, the so-called low risk and the high risk viruses, all make proteins from their E6 and E7 regions, but for some reason the most potent proteins of all come out of the HPV 16 subtype. Immune systems just don't seem to be able to fight off the protein made by HPV 16 very well, so it hangs around and causes cancer.
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.