If Anna is the lead unit in a battle in which she kills the enemy, she has a chance of obtaining Gold based on her Luck stat as the activation percentage. The amount of gold gained varies, but tends to be around 100-180 per kill.
In Conquest, Make a Killing does not activate in My Castle battles. Unlike Profiteer, another money-generating skill, Make a Killing can activate multiple times per turn (through Anna using Galeforce, being danced by Azura, or Shelter-swapping).
Ikkaku Senkin is a Japanese phrase that roughly means "one grab, a thousand gold", meaning obtaining money through little effort. It is also one of Anna's Japanese cut-in quotes in both Awakening and Fates.
Make a Killing is an english idiom used to describe making a lot of money very easily. It is also a pun on the fact that Anna needs to kill an enemy for the skill to activate.