Guilds (Artist's, Musician's, Writer's) all have two slots for specialists, which means you have to offer up population to be able to work them. When worked, these slots provide culture and Great Artists/Musicians/Writers points, which grant you one of those when you reach the threshold. When spent, they generate Great Works, which give you +2 culture and +2 tourism, which you need for the culture victory. The more population you have, the more of them you can work. (If you haven't yet, go into Citizen Management in the cities, don't let the AI do it for you - the quickest way of learning Civ well is learning to micromanage citizens.)
