Origin of Micrite = Lime Mud
Micrite is lime mud. It exists in modern environments as extremely small aragonite crystals (needles) that can only be seen clearly with a scanning electron microscope. If you were to see the sediment, however, it would have the consistency of mud.
Aragonite is a variety of CaCO3 and is a common component of pearls and some shells. Aragonite is less stable than calcite, however, and more or less quickly recrystallizes to calcite.
The orgin of micrite has a long history of debate. Originally it was thought to be exclusively of chemical origin, precipitating directly out of supersaturated sea water. During the 1970's and 1980's evidence and opinion steadily shifted all the way to a biochemical origin for micrite - the sediment coming from the breakdown of calcareous algae skeletons which live abundantly in modern carbonate environments.
More recent evidence is pointing back to some micrite being of chemical origin. This is one of those problems that is yet to have a definitive solution. Micrite, though, is probably a mixture of chemical and biochemical origin.
By the time we see the rock, however, the aragonite/calcite needles have been so recrystallized and cemented that the original nature has been destroyed. Thus, the question of micrite origin is the focus of study of recent carbonates.