What does roosevelt mean by ""speak softly and carry a big stick""?

Roosevelt means that one should use reasoned foresight in order to deal with domestic and foreign policy and act justly in every case, "speak softly," and have a strong military in order to make the adversary aware of the consequences of his possible misdemeanours.

Explanation:

Roosevelt used this peculiar aphorism in order to showcase the importance of peaceful negotiations, whilst having a strong army as backup in case something goes wrong. This bears strong resemblance with, pursuing political decisions based on particular circumstances. The aphorism I also alludes to a Machiavellian use of power when the circumstance demands. The politician should thus negotiate peacefully, according to the circumstance at hand, and intervene with military power, whenever the situation demands.