So at the 100% chance of sounding stupid. What exactly does the center diff do for me? I tried some searches but haven't looked too much.
Think about what a rear differential does. It has an input shaft (the driveshaft) and two output shafts (the halfshafts). It transmits power from the input shaft to the two output shafts, but also allows them to turn at different speeds.
A center differential is basically the same thing, but with different geometry (and without the reduction gears). The center differential has an input shaft from the transmission, and two output shafts -- the front and rear driveshafts. The center differential transmits power from the input shaft to the two output shafts, but also allows then to turn at different speeds.
When you lock the center differential, the front and rear driveshafts turn at the same speed.
When you go around a corner, the path taken by the front of the vehicle is longer than the path taken by the rear of the vehicle. Therefore, the front driveshaft needs to turn faster than the rear driveshaft. If the center diff is locked and you are off road, the tires simply slip. But if the center diff is locked and you are on dry pavement, the tires can't easily slip and that can cause stress on the drivetrain. That is why you should not drive on dry pavement with the center diff locked (or if you do, why you should not go around corners).
As to when I lock the center diff, I fish on the beach every summer. I lock the center diff before I drive onto the beach. I don't normally lock the center diff on a snow covered road unless I'm going up a steep hill or the snow is very deep.