This is an expression that was coined during Gulf War I, when Saddam Hussein invaded Kuwait. In order to ‘liberate’ the country, George Bush, the current President’s father, invited other nations to join him in his effort to overthrow Saddam.
Many countries sent troops, but there were some whose constitution did not permit them to send troops abroad. Japan and Germany, two of the closest allies of the U.S, were two such countries. Since they couldn’t commit troops to the coalition, these two rich nations did the next best thing – they gave a lot of money for the war effort! This is how ‘chequebook diplomacy’ came into being.
Nowadays, the expression is used to describe any international policy in which a country dangles money, in the form of economic aid and investment, to win diplomatic favour. Another expression that has more or less the same meaning is ‘dollar diplomacy’.
Example: China denies using chequebook diplomacy in Africa.