The MongoDB aggregation pipeline works by passing documents through a series of stages. Each stage takes the documents from the previous stage, applies a transformation, and passes the results to the next stage. For example, $match filters documents by a condition, reducing the number of documents. Then $group aggregates documents by a key and computes sums, changing the document structure. $sort orders the documents, and $project selects which fields to keep in the output. This flow continues until all stages are processed, producing the final output documents. The execution table shows each step's input, action, and output, helping visualize how documents change through the pipeline.