The document describes the quicksort algorithm through pseudocode and diagrams. It shows the steps of quicksort, which are: 1) Choosing a pivot element, 2) Partitioning the array around the pivot by swapping elements less than and greater than the pivot, 3) Recursively applying quicksort to the subarrays divided by the pivot. The document provides an example of quicksorting an array of numbers and visualizes each step of the process.