It provides a visual of military might that helps Roosevelt to argue his main point.
Explanation:
The "big stick metaphor" is a visual idea that Roosevelt uses to clarify his foreign policty strategy.
The big stick works as a tool that can work as a threat, but that can also be used to apply force, and Roosevelt's foreign policy strategy was to have foreign countries, especially those in Latin American, comply with his whishes, either peacefully (the threat), or by force.
