Kirk/Spock is a subset of Trek Fandom which choose to believe that the Captain and the Vulcan are homersexual symbiotes or something. :)
Ever since the original series was on the air, fans (mostly female at first) have written what is called "fanfic" or fan authored fictional stories about Kirk and Spock being lovers. For many years in the seventies all you had to do was whisper "KS" and Trekkers might giggle or roll their eyes. Don't get me wrong, they were tolerant for the most part, but it still seemed like a taboo subject matter. Like the female generated fanzine that included a nude foldout watercolor of Spock in the seventies. Unusual. Nowadays this kind of stuff seems quaint and belonging to the Victorian era or something. Of course K/S has spawned any number of fanfic subjects that play "what if" with all sorts of combinations on all sorts of shows, but the K/S'ers blazed the way! Pants Off To 'Em!