Fireplace - concrete base repair
That cracking was caused by the original fireplace cement not being allowed to cure long enough. A little moisture trapped in the concrete and the HOT flames generated steam and caused the top coat on the base to spaul. You could just break it all up with a three pound hammer, clean it out real well and pour a new floor, but you should probably get a good brick mason in there to look it over. The brick fireplaces they put in around here use the same fire brick you have on the walls of your fire box, all across the base of the fire box.