DPI only really comes into play for the most part when printing.  though you can do DPI for screen its going to vary based on things on how the manufacturer set that up.  Retina display for example on an Ipad higher DPI over the same inches.

if your screen is set at 72dpi then a 1000x1000 with a 72dpi is going to look the same as a 1000x1000 96dpi because the program is simply going to display a 1000 pixels the same way.  if you render an image at 10" x 10" at 72 dpi then that is 720x720, at 96dpi then it is 960x960. 

It comes into play when printing more.  people start talking whats the acceptable level the eye can see.  Some people can see the difference between 100-150dpi vs 300dpi some can't, some 200dpi looks printed about the same as 360dpi.  It also depends on whats being printed, the types of edges and colors.  I know a person who paints on an ipad with an app that supports a max of 4096x4096 (he didn't paint this one that high) who made a nice larger than 16x20 print by enlarging using software from OnOne (that resize that was mentioned above in fact) that retains the edging and essense instead of pixallating it.