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In this video, the presenter explains the insertion sort algorithm in computer science. The process begins at index 1, where the current value is stored in a temporary variable named "temp." The algorithm then examines the elements to the left. If any element is larger than "temp," it is shifted to the right; the process continues until a smaller element is found or there are no more elements to compare. Once the appropriate position is found, the value in "temp" is placed there. The presenter moves on to the second iteration, repeating the same steps: storing the current value in "temp," comparing with left elements, and shifting larger ones to the right if necessary.