> the insight
The vertices will be on pixel addresses. The edges of the triangle will have no discontinuities themselves, and the triangles sharing an edge will have no discontinuities. Hence, no banding or blockiness. A naive renderer would just render the colors of the triangle as a straight linear interpolation. A more advanced one could look at the adjoining triangles, and render it so the first derivative would also be zero across the line. I.e. curve fit it.
The selection of where the vertices go would likely be best selected where the colors are shifting fastest, i.e. an edge in the picture.
The neato thing is one could render a low res image on a high res display and it'll still look good. You wouldn't have these stray pixels scattered around the text like jpg does. The other neato thing is more vertices can be put in the complex areas of the image, rather than wasting bandwidth on the parts of it that are smooth.
Progressive sharpening of the rendering also works, as more vertices can be added at any time.