I didn't look at the figure you quoted, but it sounds like the mast rotator. It controls the amount the mast can rotate. The mast can bend more side to side, depending on how the diamond wire are tensioned, than front to back. More rotation equals a flatter sail with heavy mainsheet tension. It's something you develop a feel for. More rotation when you are overpowered, and less when you need more power. The mainsail has a shape built into it with a curve at the front (luff). Pulling the luff curve forward flattens the sail. This is more easily done by bending the mast, which bends more side to side.
The outhaul line is one of those things I figure out when I need to.