The word I wanted was auxin.
“Both girdling and notching interrupt the downward movement of the plant hormone, auxin, through the phloem (inner bark). Auxin is produced in the shoot tips and moves down the phloem, preventing the growth of lateral buds. This phenomenon is especially characteristic of apically dominant species such as cherry, pear, and to a lesser extent, plum [And Sage!! – Anne] . The bud or buds immediately below the removed bark strip are therefore released from the influence of the auxin and will usually begin to grow.”
Tips have auxin in them. Auxin flows down and stops the buds growing. When you pluck the tips, there’s no auxin, the buds grow, and you get more sage/basil/whatever. Thanks, Chuck Ingels, Farm Advisor! Thanks, Google!