Human Papilloma Virus. Source: Center for Disease Control.
Of the 170+ varieties of HPV just two (HPV 16 & 18) are linked to most (70% of cases of) cervical cancer in women. These two also may cause throat and penile cancer in men and 90% of anal cancers in both sexes are caused by these two.
The HPV vaccination gives immunity to these two but is recommended for pre-adolescents. HPV 16 & 18 do not cause genital warts. The vaccine will not protect against all HPV cancers but most.
If you have or ever had common warts (verruca vulgaris) or plantar warts they are also HPV just not 16 or 18.
Genital warts are usually HPV6 or HPV11 and are most commonly transmitted by anal or vaginal sex but can be transmitted by any sexual contact. They are not linked to HPV cancers.
Wear condoms, people. Wrap it up.
The ladies already know to get regular Pap smears with their OB/GYNs.