It means to practice kindness and goodwill, particularly in diplomacy between nations, but to be ready with a strong military as both a warning and in case it is needed. For Theodore Roosevelt, the "big stick" was a powerful navy.
" and you will go far".
Theodore Roosevelt originated this phrase as a description of his foreign policy when he was President of the United States. Roosevelt attributed the proverb to West Africa,...
Theodore Roosevelt said "Speak softly and carry a big stick" when he referred to his Naval expansion policy.
http://en.wikipedia.org/wiki/Theodore_Roosevelt#Quotes