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This article provides a pedagogical explanation of singular value decomposition (SVD) and its application to image compression. It starts with a mathematical definition of SVD for any matrix, then demonstrates how SVD can decompose an image into a weighted sum of outer products of 1D vectors. By sorting the singular values and reconstructing the image using only the largest ones, the article shows how progressively better approximations of the original image are achieved. A grayscale image example illustrates that even with 100 out of 512 vectors, the reconstruction closely matches the original. The explanation highlights how horizontal and vertical features are captured first, making SVD a powerful tool for compression and analysis.