The SVG coordinate system plays a crucial role in defining the position and size of shapes within an SVG image. It functions on a two-dimensional plane, with the origin (0,0) at the top left corner. The x-axis increases to the right, while the y-axis increases downwards. Each unit corresponds to a pixel in the output device for raster graphics. Transformations can be applied to shift, rotate or scale objects within this system without loss of quality due to its vector nature. This allows for high-resolution rendering across different display sizes, making SVGs ideal for responsive web design.