I think this is a type of cryptocrystalline quartz, which we could probably refer to as agate. The blue colour arises from impurities, and I suspect the little flecks do too - through metamorphic alteration, perhaps of the same impurities. What the flecks are is difficult to say. The opalescent parts are probably due to optical intererfence effects in thin slivers (there will be a thin crack just behind where you see the opalescence). If you look up 'Newton's rings', you'll get more of an idea about that.