DPI is a term that deals with the pictures quality. It stands for Dots per inch (or pixels) And is representative of how many dots are rendered per inch of space. For most cases you use the 72 dpi and 300 dpi settings.
72 dpi is typically used on computer screens. It is a lower resolution but is usually perfectly fine for computer screens. Its all relative to size. Say you have a 1280px screen and the screen is 21 inches, 1280/21 yields so you have 61 dpi.
Alternatively 300 dpi is typically used in printing. Printing paper is able to fit 2550 dots on 8.5 inches of space. So by doing the simple math shown above that equates to 300 dpi. So for the most part, dpi is a representation of image quality. Though what you are doing determines determines what dpi you need to use.
James Bobbitt's Blog 