Iolite is the gem name for cordierite, and the property it is known for needs explaining properly, because it is the basis of every claim made about the stone.
Pleochroism is the absorption of light differently along different crystallographic directions. In a mineral that is optically biaxial, as cordierite is, there are three principal directions and therefore up to three distinct colours, which is called trichroism. Cordierite is the standard textbook example: turned in the hand, a single crystal shows a strong violet-blue down one axis, a much paler yellowish or colourless tone down another, and a pale blue down the third. The change is dramatic and requires no instrument.
The mineralogical basis is straightforward. Light in a crystal resolves into components vibrating along the principal directions, and if the iron in the structure absorbs one component more strongly than another, the colour seen depends on how the crystal is oriented to the eye. Tourmaline, kunzite and andalusite all show it; cordierite shows it most.
This is what a cutter has to manage. A badly oriented iolite is grey or yellowish; a well oriented one is a clean violet-blue. It also caps the size of good cut stones, since the orientation that gives the best colour may not be the orientation that gives the best yield from the rough.
Cordierite is otherwise a common metamorphic mineral, an indicator of low pressure and high temperature conditions, and it is far more often encountered by geologists in a thin section than by anyone in a ring.