A partition of a positive integer is a way of writing that integer as a sum of positive integers. The document provides an example of the 5 partitions of the number 4: 4, 3 + 1, 2 + 2, 2 + 1 + 1, 1 + 1 + 1 + 1. It asks the reader to find all 15 partitions of the number 7, listing them out.