Gypsum is a common calcium sulphate mineral. It often occurs in evaporite deposits in arid areas (places where the moisture evaporates faster than it builds up). It often breaks along cleavage planes, giving a pearly lustre on the cleaved faces. Sometimes it forms as 'fish-tail' crystals, twins that resemble, well, fish tails! It is a very soft material, softer even than your finger nail which will scratch it!
The specimen pictured is from South Australia, probably from the Mt Gunsen area.