Jyeshtha means the eldest. In an Indian family that word carries weight: the eldest gets the authority and also gets handed the problems, the bills and the responsibility for everyone younger.
In Hindu mythology, Indra is the king of the gods. What makes him the right deity here is that Indra's position is never secure. He wins his throne, he defends it, and the stories are full of moments where he nearly loses it. This is authority that must keep proving itself, not authority that can relax.
The three symbols say the same thing from different angles. An earring and an amulet are marks of rank and of protection. An umbrella shelters whoever stands under it, and it also blocks their light, which is a fair description of how protective people sometimes operate.
Its shakti (the special power a nakshatra carries) is rising and conquering, meeting a challenge with courage. Jyeshtha does not avoid a fight it thinks is necessary.
Jyeshtha is known for responsibility, protectiveness and a quick eye for threats. Natives often end up carrying a family or a team earlier than they should have. Many are the eldest in some real sense even when they were not born first. The Hindu month of Jyeshtha is named after this star.