I assume you mean "The Influence of Sea Power on History" written by Admiral Alfred Thayer Mahan. Mahan had argued that a nation's greatness depended upon its sea power. He further argued that if the U.S. were to achieve that greatness, it would need a modern steel hulled naval fleet, a coaling station in the Pacific Ocean to allow refueling of ships traversing that ocean, and an isthmian canal to shorten transit time between the Atlantic and Pacific. This work was influential in U.S. involvement in construction of the Panama Canal. Although it also bears strong relationship to U.S. annexation of Hawaii, Hawaii's annexation was more directly the result of American sugar planters on the Island who overthrew the rightful Queen with the assistance of American military forces.
The White Man's Burden, by Kipling, was written following the Spanish American War and America's annexation of the Philippine Islands. It contained the subtitle, "The United States and the Philippine Islands." Many, including the American Anti-Imperialist League, opposed the annexation. Kipling's poem indicated that the U.S. as the bearer of true "civilization" had the burden to carry that civilization to the people of the Philippines. It is a classic example of the long-held belief in the superiority of Christian Anglo-Saxon culture:
Take up the White Man's burden--
Send forth the best ye breed--
Go bind your sons to exile
To serve your captives' need;
To wait in heavy harness,
On fluttered folk and wild--
Your new-caught, sullen peoples,
Half-devil and half-child.
Expansionism is a set of policies and priorities that focuses on the aquisition of territory and new markets, usually oversees, in order to expand resource aquisition and a countries economy. The creating of colonies or the dominating of less developed nations through puppet governments could also be included in an expansionist strategy.
"White Man's Burden" was a poem by Rudyard Kipling that helped support expansionist policies. In short, it justified expansionism because people felt it was the duty of "more civilized" western cultures to bring Christianity and superior cultural institutions from the west to all the peoples of the world. It was the duty or "burden" of white men to help backwards, primaitve peoples reach civilization.
"A Naval Power" argues that in order for the U.S. to become a world power and take more of a central role in world politics, the U.S. must develope a strong navy and aquire territories around the world that can serve as ports.
Both of these arguements support expansionism.