The term "military reparations" refers to payment for damages made in recompense for damages due to acts of war.
The most famous example of military reparations is the long list of punishment and repayments for Germany in the Treaty of Versailles at the end of World War One. This treaty, and its debilitating conditions, have been listed as one of the major causes of the Second World War, in that Germany had become so humiliated and crippled by the war reparations, that Adolf Hitler was able to seize power and plan revenge.
The obvious link to the Treaty of Versailles is the humiliation of France at the Treaty of Frankfurt (1871), which saw France occupied and in debt of 5 billion gold francs. It would seem that France (in 1919) wished to return the favour bestowed upon them by Germany.
In ancient times, Rome inflicted harsh penalties on Carthage after the First and Second Punic Wars. Greece paid large sums in reparations to Turkey after their war in 1897.
To add on a bit about the war reparations after the First Punic War, the war reparations Rome demanded influenced the sphere of Carthaginian politics in more ways than one. Hanno II the Great refused to pay the mercenaries the amount that was promised, partly due to the inadequate funds after the war. This angered the mercenaries and led to the two-year Mercenary War, where the mercenaries led a revolt against Carthage with the help of Libyans who were unhappy living under Carthage's rule.
Another step Carthage took to help pay the war reparations was to start a series of campaigns to gain control the Iberian peninsula, which was plentiful in silver. Their campaign eventually led to the conquest of Saguntum, a city protected by Rome on the Iberian peninsula, and this led to the Second Punic War.
It's interesting to see that you can see the parallel of one war's reparations leading to another war in the First and Second Punic Wars, similar to World War I and II, even though it happened 2000 years earlier.
Some war reparations include changes in money policies like the French payment after the Franco-Prussian war which led to a major decision by Germany to move on to the gold standard. This is also the same for Japan's decision to join the gold standard. In WW1, Russia agreed to pay the reparations to the Central Powers when Russia left the war in the Treaty of Brest-Litovsk. Bulgaria had to pay reparations of 2.25 billion gold francs to the Entente.