PPI stands for "Pixels per inch" and is almost exclusively used for printing, not video display. If you take an image that is 800 pixels wide and 600 pixels high, and you print it with a PPI setting of 100 pixels per inch, the print will be 8 inches wide by 6 inches high. If you print at 200 PPI you get a print 4" wide by 3" high. Now the print at 200 PPI will be higher in quality but smaller. Most people seem to agree that around 320 PPI is the highest number you really need. Above that it's very hard to see any improvement in image quality. 240 PPI is often used and even that is often regarded as high quality. Most people notice a quality drop when they go much below 180 PPI.
DPI stands for "dots per inch" and is a property of a printer, not a digital image. It's a measure of how finely spaced the droplets of ink can be in a print. However the number is a bit misleading since it's not always measured in the way you think it might be! Printer settings of 360dpi, 720dpi, 1440dpi and 2880dpi are often found. However the difference between then is subtle at best. Most people probably couldn't tell the difference and 360dpi usually looks great. Changing DPI does not change the size of the print. PPI controls that. DPI controls print quality (though as I said, over 360dpi you typically don't see much change).