The origin of the social web is various, but the origin of the term is attributed to Howard Rheingold.
The term “social Web” was coined by Howard Rheingold for this network in 1996; Rheingold was quoted in an article for Time on his website “Electric Minds”, described as a “virtual community center” that listed online communities for users interested in socializing through the Web, saying that “The idea is that we will lead the transformation of the Web into a social Web”. (wikipedia)
It’s worth noting that the use of HTML forms (crucial in wiki as well) was key here. Forms became the way to hack a read/write web together.
The HTML form was born in the curses browser. See Birth of the Form.