This place is accessed after obtaining the Amaranth Badge. You can access it north-west of Tourmaline Desert. Passing through the cave will lead you to Teknite Ridge. You can also come here using Rock Climb in Beryl Cave, but it brings you into an entirely different section.
Head to Beryl Cave and use Rock Climb in the upper area. This will lead you all the way to Teknite Ridge. Go into the cave and you’ll be prompted to use a move. Use Dark Pulse in battle to change the field, then use Rock Smash to break into another area. In the area, you’ll have the opportunity to battle a Volcarona and later catch a wild Larvesta.
Teknite Cave is named after tektite, a form of dark natural glass that is created by meteor impacts. This "meteor glass" is formed when the meteor impact on land hurls debris through the air and melts it while in the air.