Thorongil, Sindarin for Eagle of the Star (thoron meaning eagle and gil meaning star), was an alias for Aragorn. Another of Aragorn's names is Estel, meaning hope, so a six-pointed star was used as a reference to the Star of Eärendil, an enduring sign of hope in Middle-earth. The eagle rests on a black field, pulled from the standard of Elendil.
"Aragorn undertakes his great journeys and errantries. As Thorongil he served in disguise both Thengel of Rohan and Ecthelion II of Gondor."
—Excerpt from Appendix B of The Lord of the Rings
"...[Ecthelion II] had the advice of a great captain whom he loved above all. Thorongil men called him in Gondor, the Eagle of the Star, for he was swift and keen-eyed, and wore a silver star upon his cloak; but no one knew his true name nor in what land he was born. He came to Ecthelion from Rohan, where he had served the King Thengel, but he was not one of the Rohirrim. He was a great leader of men, by land or by sea, but he departed into the shadows whence he came, before the days of Ecthelion were ended."
—Excerpt from Appendix A of The Lord of the Rings