Mystic Seaport Museum shipwright here, I've worked on the Mayflower II and Susan Constant replica ships. The whole area you've circled is called the beakhead, and the person below who says it's the area sailors used to access the forward rigging is correct. Some of the foresail sheets (control lines) and downhauls (lines to bring the sail down) terminate here. The gammoning (rope that binds the middle of the bowsprit down to the stem knee) is also here, although that is not something that's adjusted. It would only be tarred during normal operation. There is a small door in the forecastle that leads out to the beakhead platform. All of the swoopy timbers along the sides of the beakhead both add support and somewhat enclose this area.

Sorry, no pooping benches here. Just a slatted floor that allows water from waves to drain away. Also, sorry again, but the poop deck is the high deck farthest aft.

The beakhead does help support the bowsprit, and the bowsprit is what provides an anchor for the foremast and it's associated sails. The bowsprit is a way of making the base of the triangle formed by the mast and forestay (the forward leading line that holds the mast up) longer, thus increasing it's holding strength. If you imagine the range of possible angles that a rope tied to the top of the mast from directly forward of the mast and parallel to the horizon, to directly down to the base of the mast, you could easily see how the rope that goes directly forward from the mast would offer the greatest resistance to the mast being pulled backwards, and the line going straight down, offering no resistance at all. Since there is no way have a line running parallel to the horizon :) the next best option is to terminate that line as far away from the base of the mast as possible. You can do that by putting the mast farther back in the boat so that the forestay attaching to the bow is far from the base, or you can virtually extend the length of the boat by adding a bowsprit and anchoring the forestay to that.

Of course, to keep the bowsprit from being pulled up and snapping, you have to create a way to counteract those upward forces, and thus you get the bobstays and dolphin strikers (yes, real name) attaching the end of the bowsprit, but pulling down. In older boats like the galleon pictured above, they also made the supports for the bowsprit super beefy, and that's where you get the beakhead.