"Sovereignty" means control over one's own nation or territory.
Hawaii was concerned with sovereignty in 1884 because in that year the Kingdom of Hawaii was signing a treaty that gave the United States "the exclusive right to enter the harbor of the Pearl River in the Island of Oahu" (in other words, Pearl Harbor), "and to establish and maintain there a coaling and repair station for the use of vessels of the United States, and to that end the United States may improve the entrance to said harbor and do all other things needful to the purpose aforesaid." (You can tell I'm quoting from the actual treaty there.)
When the treaty was reaffirmed and extended in 1887, King Kalaukaua of Hawaii said to the Hawaiian legislature that his government had assurances from the US government that the treaty did "not cede any territory or part with or impair any right of sovereignty or jurisdiction on the part of the Hawaiian Kingdom."
Ultimately, however, in an age when imperialism was common throughout the world, the United States did take over control of Hawaii. In the late 1800s, the US supported American sugar planters who overthrew the Hawaiian monarchy, and by 1900 Hawaii became a US territory.
