It often refers to a nation's display of military strength or economic pressure on others. The UN doesn't shy away from using the big stick in the form of sanctions.
Pro Tip 2/3
Implied Threat
Used to hint at power behind diplomacy without displaying it openly. The prime minister's stance is patient, yet the big stick remains firmly in his grip.
Pro Tip 3/3
Teddy Roosevelt
The phrase is famously attributed to Theodore Roosevelt's foreign policy: 'Speak softly, and carry a big stick.' Modern leaders often cite Roosevelt's big stick policy as an influence.