That space is surrounded by water. This is what (effectively) keeps the entire firebox from melting from the heat of the burning gas. Above the firebox's "crown sheet" (top) is the area occupied by steam, which then gathers (ultimately) in the steam dome (highest point of the whole boiler) and fed via the throttle and dry pipe to the cylinders. Again, if the crown sheet is not covered in water, it too will fail, and bad things will happen.
The mud ring is the lowest point of the boiler, so it is always full of water. It is also where all the sediments in the water settle, etc.
(@Jason, how'd I do? :-)