PPI and DPI are a constant and seemingly eternal source of confusion. Knowing the difference between the two is important and is really easy to understand.
A pixel has a variable size.
Let's say you look at an image that is 900 x 675 pixels large on your computer's monitor display. The dimensions of the displayed image depend on the native resolution of the monitor display. The higher the resolution of the dipslay, the smaller the image will be displayed, because the image size as measured in pixels does not change. Conversely, on a monitor display with lower resolution, the same image will appear larger. Remember, pixel size is a variable.
Because monitors have native resolution, it is usually around 100 pixel per inch (PPI), we always size images for monitor display and Web use in pixels. We never use inches or centimeter, and we never talk about image resolution.
You can easily verify that a pixel has variable size. Open an image, then change the screen resolution. If you increase screen resolution, the image will get smaller, if you decrease screen resolution, the image will get larger. Most likely your monitor is set to its highest resolution, but you can set a lower resolution and see how the image will appear larger.
Pixel Per Inch denotes a constant size.
Let's say you want to print a 5x7 inch image in photo quality. You have to scale your image not only in terms of dimensions, but you also have to size the image in terms of resolution. As a general rule, you need about 300 pixels per inch (PPI) resolution in order allow for a print in photographic quality at "normal" (that's of course arbitrary!) viewing distance. At 300 PPI, each pixel is so small (1/300 inch) that the human eye can't resolve all the individual pixels. The image appears to have continuous tones. Remember how I earlier said a pixel had a variable size? That is still valid. However, at any number of pixel per inch, each pixel has a constant size.
What about Dots Per Inch?
Dots per inch (DPI) refers to only to printer head output resolution. All modern printers have native output resolution that approaches or exceeds the requirements for printing in photographic quality. Don't worry about DPI.
What's the relevance of Dot Per Inch then?
The printing resolution (DPI) should be at least twice as high as the image ressolution (PPI). For example, you might state that you want this 16x20 inch 300 PPI image printed at least at 600 DPI. Since almost all printers have at least the capability of printing at 600 DPI or better, as previously stated, DPI is usually nothing to worry about.