Kyanite is a gem only incidentally. Its real importance is as one of three minerals that tell a geologist what a rock has been through.
Kyanite, andalusite and sillimanite all have the composition Al2SiO5. They are polymorphs: identical chemistry, three different crystal structures, and each is stable over a different range of pressure and temperature. Finding one of them in a metamorphosed aluminous rock therefore constrains the conditions under which that rock recrystallised, and finding the boundary between two of them in the field maps a line of equal pressure and temperature across a mountain belt. Kyanite is the high-pressure member of the three, so kyanite-bearing schists indicate burial to considerable depth.
The three meet at a single point on a pressure and temperature diagram, and the position of that triple point was argued over for decades because so much depended on it. It is one of the most experimentally studied equilibria in metamorphic petrology.
Kyanite is also a substantial industrial mineral. Heated, it converts irreversibly to mullite and expands, which makes it valuable in refractory bricks and in the ceramics that line furnaces, and most kyanite mined is used this way rather than cut.
The property that gemmologists know it for, hardness of roughly four to five along the length of the blade and six to seven across it, follows from the same anisotropic structure that gives it the platy habit, and it makes the stone genuinely awkward both to cut and to wear.