Ardra means wet, and the wetness is a storm breaking. Think of the hour before the first rain in June. The air is heavy, nothing moves, and everyone is irritable. Then it breaks, and afterwards the ground is soaked and the heat has gone. That whole sequence is the star, and the relief at the end belongs to it as much as the violence in the middle.
The teardrop carries the same double meaning. A tear is grief. It is also what finally comes out after a long stretch of holding everything in, and what follows it is usually the first honest conversation anyone has had in months.
In Hindu mythology, Rudra is the fierce Vedic storm god who later becomes Shiva. He howls, he destroys, and he is also a healer. Rudra removes what cannot continue, and that removal is closer to surgery than to punishment.
Ardra is closely tied to Shiva worship. In Tamil Nadu, the festival of Ardra Darshan, or Thiruvathirai, falls when the Moon is in this nakshatra in the month of Margazhi. It celebrates Shiva as Nataraja, the lord of the cosmic dance. That dance is exactly what this star describes: destruction and creation happening in the same movement.
Its shakti (the special power a nakshatra carries) is effort that achieves, the success that comes out of the difficult part. Ardra is known today for research, technology and any work where you have to understand why something broke.