Scientific

Calcite is a mineral with the formula of CaCO3.  It is extremely common being found throughout the world in all types of rocks, most commonly in sedimentary and metamorphic rocks but also in igneous rocks as well. Calcite is the principle constituent of limestone and marble; it forms the shells of sea creatures and the shells of coral making up reefs.  It can also be deposited by chemical precipitation.  It can be found as large deposits so clear you can see through it (islandic spar), translucent and colored as in marble, or very plain large limestone cliffs ubiquitous throughout the world.  Calcite itself is relatively soft and can be easily scratched. It forms many cave structures as it dissolves in water (hard water), then deposits quickly when the water is evaporated.  It forms prismatic crystals known as aragonite or cave calcite which can be quite elaborate.

Uses

As limestone and marble, calcite has been used as a building material for millennia. Limestone that has been crushed and heated is called lime and is the principle component of cement. When lime is moistened and allowed to dry, it quickly crystallizes into calcite binding the other material (sand and gravel) together into a solid mass known as concrete.  It is probably the most common neutralizer of acids and is spread on fields as an acid neutralizing soil treatment, called aglime. Crushed limestone can be dispersed in streams to combat acid runoff from mining operations.   High purity limestones can be crushed, mixed with sugar and flavoring and made into chewable tablets to neutralize stomach acid, and is also an ingredient in numerous other medications used to treat digestive and other ailments.  Calcium, the primary element in calcite is essential to the body.  On the other hand, calcium is the primary ingredient in kidney stones and is also found in gall stones. 

It is used to neutralize sulfur emissions when burning fossil fuels.  In powder form calcite is often extremely white in color and can be used as a pigment.  And some of the earliest paints used powdered calcite.  It is the primary ingredient in white wash, and is still used as an inert ingredient in paint.  It is fed to chickens and cattle to produce harder egg shells and milk.  Because it is softer than stone, porcelain, and most plastics used as counter tops, but harder than dried food and other debris that need to be removed, it makes an effective non marring cleaner for kitchens and bathrooms, except for marble fixture which are the same hardness.

Meaning

Calcite is known as a powerful amplifier and cleanser of negative energies from the environment. It brings forth a polarizing prismatic energy, releasing a spectrum of energy to clear and activate all the chakras. It is a spiritual stone that facilitates the opening of higher consciousness and psychic abilities. 
Calcite calms the mind, teaches discernment, stimulates insights, and boosts memory connecting the emotions with the intellect. It is an excellent stone when studying the arts and sciences and for helping the mind and body to remember soul experiences.