An iconic landmark, seeing this statue is probably in the top five on every visitor's Oahu to-do list, alongside the Arizona Memorial, Waikiki beach, and the Diamond Head hike.
You probably already heard the story about how the first commissioned statue was lost at sea enroute to Hawaii from Europe, how a second statue was cast (the one here), and how the original was later found and is now displayed in Kamehameha I's town of birth on the Big Island. A third statue is at the U.S. Capitol, and a fourth statue was commissioned by Princeville Resort, rejected by the people of Kaua'i (Kamehameha I never conquered Kaua'i as he did the other islands), and is now in Hilo. Apparently the fifth and most realistic statue is at the Grand Wailea on Maui, and there is a sixth one in Las Vegas!
Kamehameha I ("Kamehameha the Great"; 1758-1819) is known for conquering all of the islands in Hawaii, except Kaua'i where they formed a peaceful agreement, and unifying the islands under a single rule as the Kingdom of Hawai'i by 1810.
One of the motifs on the base of the statue depicts the "Law of the Splintered Paddle" (Ke Kānāwai Māmalahoe), which Kamehameha I articulated to ensure the free and peaceful travel of his people and the right to lie down to sleep next to the road without harm. Now we have the opposite, the sit-lie ban.
You can find out more about this statue - information you can't get off Wikipedia or off the statue itself - inside Ali'iolani Hale (the building behind the statue in the back of everyone's photos). In front of the Judiciary History Center inside Ali'iolani Hale there is a brochure you can take with information about the statue. There are also exhibits about it if you have time to browse the Center. Highly recommend the Judiciary History Center! You can see what Honolulu looked like in the mid 1800s and learn much about Hawaii history and the architectural history of Ali'iolani Hale.