History of 72dpi
The term 72dpi goes back to the early Apple computers (Macs). The early Macs were setup to represent points as pixels on screen. Points are the printer's way of measuring type sizes; they are very nearly 1/72nd of an inch. The early apple monitors were designed so that 1 pixel was approximately the size of 1 point, as such Mac programmers got used to points=pixels, hence 72dpi or 72ppi.
The term has continued until today and “72dpi” has become standard industry terminology. It is now common practice when designing for screen based media to create images at 72 dots per inch (or 72 pixels per inch).
This concept is carried across other technology with digital cameras and many graphical applications (such as Adobe Photoshop, and Adobe Fireworks) which have the default resolution for web ready images set to 72dpi.
The myth of 72dpi
The Myth of 72dpi Unfortunately with advances in technology, (changes in screen sizes and resolutions) a resolution of 72dpi (72 dots/pixels per inch) is no longer accurate, but the term and use of 72dpi remains.
Infact the DPI that is used for an image in any screen based media (e.g. a web site, mobile website or mobile app) doesn't matter. You could use a 300dpi image or a 2dpi image and get the same result on screen; it's the pixel dimensions set for the image that really count.
This article provides a great explanation of image resultion for the web. webdesignerdepot.com