Refering to men or women that are of interest to the opposite sex. The person comes across amuseing, and could possibly be a potential mate. But until that is known, the person is referred to as a "possibilitie".
A woman walks into a bar and notices right away that there are many goodlooking men that she would be interested in. These men are called possibilities. They just might possibly have looks and a personality to offer, but thats to be determined.