Virility is a fancy word for "manliness." You could demonstrate your virility by lifting a minivan, but why be a show-off? Your virility also means that you'll need a minivan to cart around your many children.
The Latin virīlitās, from vir, or "a man," is the base for the word virility. You can also use virility to refer to "macho" qualities that might seem to reflect outdated notions of masculinity. French feminist author Simone de Beauvoir once wrote, "No one is more arrogant toward women, more aggressive or scornful, than the man who is anxious about his virility.”