Answer: Thedore Roosevelt used this expression to describe style of American diplomacy. This diplomacy was supposed to be an extension or expression of principles of "Monroe doctrine" (to keep Europeans and especially British away from Americas). Roosevelt used this expression shortly before the death of the president William McKinley (1901) meaning that USA should protect their economic interests in Central and South America. Diplomacy of "Big Stick" led to American expansionism.
Explanation: Diplomacy of Bick Stick is sometimes understood as "Diplomacy of Dollar". It led to expansion of American Navy and involvement of USA in international affairs. In this context one can speak about Canal in Nicaragua or Canal in Panama that were supposed to facilitate American manoeuvres in Central America and Carribean.
