DPI and PPI are terms used when referring to image quality and resolution.
DPI (Dots per Inch) is a traditional design term that came from the printing world. If you look closely at any design printed using a 4-color process, you'll see a halftone pattern of overlapping dots of four colors: Cyan (C), Magenta (M), Yellow (Y) and Black (K). The more dots included, the better quality image will result.
PPI (Pixels Per Inch) is a more modern term used to discuss images viewed on a screen. The same concept applies, but in terms of pixels instead of the 4-color process.
We like to think of DPI and PPI in the same way as a bowl of cereal. Once you pour a bowl and close up the bag, you can only take cereal away, not add to it. You'd have to start all over making a new bowl with more cereal to have more. It's the same with an image; once it's captured, it contains the most pixel data it will ever contain. Once reduced, the extra data can't be brought back in its original form.
Note: New technologies are emerging that utilize algorithms to generate lost pixel content, increasing the resolution. We're keeping our eyes peeled for updates on this exciting new endeavor.