Vincian is a proposed identity to be used by homosexual men (men who feel attraction to other men). Due to the fact that "gay" has become a term for the entire LGBT community, there wasn't a term specifically for homosexual men. For this reason, this proposed term was coined for homosexual men who wanted their own identity. The gay female counterpart is lesbian.
Etymology
The term vincian was coined in honor of Leonardo da Vinci, who was an Italian polymath of the Renaissance. He was thought to be involved in various homosexual relationships.