An exhibitionist is someone who shows the genitals to an unsuspecting stranger, without any attempt to have sex with that person.
The response that is hoped for is either surprised pleasure and amazement or fear and panic. Indifference won’t satisfy the exhibitionist.
In the Netherlands exhibitionism is illegal, it’s a criminal offence.
For male exhibitionist there’s a special term: ‘flasher,’ while for women no such term exists.
The term exhibitionist is also used more informally for everyone who finds it exciting when others see (part of) their body. This concerns many people, varying from girls showing cleavage and wearing short skirts to male strippers and actors who like to do nude scenes. It’s the game of lust, based on looking and being looked at, which is a important part of sexuality.

See also: voyeurism