The boiler will explode only if the pressure inside exceeds the capacity,but there is a safety valve to take care of it.
Every boiler normally has a low water safety which interupts fuel supply below the safe water level. Your boiler is so far unidentified (fire tube, water tube, box/jacket, etc.). Low water firing (if permitted to occur) usually results in leaking at a minimum, and more likely cracks, warping and destruction. Rupture of the boiler is unlikely (but not impossible) while some water remains.
Boilers have a balance between the heat supplied to them from the burner(s) and the heat removed by the steam. The temperature of the burning fuel is usually much hotter than the melting point of the boiler material, usually steel. But the steaming water actually cools the boiler steel, keeping its temperature just above the temperature of the boiler's steam/water mixture. So if you lose the water, you can damage the boiler. I have actually seen the results of this happening. Due to a malfunctioning water control system, this boiler did not get enough water and the boiler's tubes actually melted because the burners did not stop like they were supposed to. Not pretty.
