Andrew Dacey has written a nice explanation of this on his site. To summarize, here are a few points:
All that PPI does is affect the print size of the image.
DPI only refers to the printer. Every pixel output is made up of different coloured inks (usually 4-6 colours, although many printers use more now). Because of the small number of colours, the printer needs to be able to mix these inks to make up all the colours of the image. So each pixel of the image is created by a series of tiny dots (you could think of them as sub-pixels). Generally, the higher the DPI, the better the tonality of the image, colours should look better and blends between colours should be smoother.
Higher = better for both, with most screen images at 72 PPI and print graphics typically in the 300-600 PPI range.