Today it means: A hypothetical problem dealing with the notion of infinity. Given an empty vase and an infinite supply of balls, an infinite number of steps are performed, such that at each step 10 balls are added to the vase and one ball removed from it. The question is then posed: how many balls are in the vase when the task is finished? Full definition →
The problem was originally described by mathematician John E. Littlewood in his 1953 book Littlewood's Miscellany, and later expanded upon by Sheldon Ross in his 1988 book A First Course in Probability.
Etymology from Wiktionary, CC BY-SA 4.0.