The array_walk function in PHP takes an array and a callback function. It goes through each element of the array one by one. For each element, it runs the callback function. If the callback changes the element by reference, the original array changes. In the example, each number in the array is doubled. The execution table shows each step: starting with 1, doubling it to 2, then 2 to 4, and 3 to 6. After all elements are processed, the function ends. This helps understand how array_walk modifies arrays by applying a function to each element.