Simply put? Nothing.
Well, if that were all I had to say on the subject, this would have to be my shortest blogpost ever… Okay, a bit more info then:
A lot of first time DSLR users are concerned that their shiny new camera delivers files that are “only” 72dpi, while their old point and shoot delivered 300dpi files. Why is this concern unwarranted? Surely 300 is more then 72, and more is better, right?

Wrong

The old wisdom saying is that “300dpi is for printing and 72dpi is for screen”.
There are a few things wrong with that.
First and foremost, the term “dpi” stands for dots per inch. In a digital file there are no dots, only pixels. So the correct term is pixels per inch (ppi).
Also, 72ppi originated as it was the resolution of an ancient Mac monitor. Current monitors have a much higher pixel density: My old 12″ PowerbookG4 for instance has a screen resolution of about 100ppi. Most current screens are somewhere between 80 and 120ppi.

Do the math…

for your screen: Simply measure width and height and divide the number of pixels by the measured values… Tip: Once you found the figure for your screen, be sure to enter it in the PSCS4 preferences under “Units and Rulers, Screen resolution”: That way, the “Zoom, Print size” will show an accurate sized preview.
So, is a 300ppi file better then a 72ppi file?

No difference

If you hadn’t gathered as much from the above, for display on screen, only the display you’re using will determine the “resolution”.
So, a file that contains for instance 500×750 pixels will be displayed at a different size (in inches, centimeters, or whatever you prefer), depending on the screen you’re using to view it. The arbitrary ppi figure set in the file has no relevance whatsoever.

To illustrate that, here is an example: Each file is 500×750 pixels. One is 72ppi, the other 300ppi.

Notice the difference? No? That’s because there isn’t any.

Why use it then?

Because you have to put something in the box: There is no way that Photoshop will allow you to not fill in a value. However, what you put in there is pretty arbitrary. Use whatever you like basically for display on screen.
I prefer to use 300ppi for general use, since then the “image size” dialog box will quickly tell me about how large I can print an image at decent quality. For web, I mostly use 72ppi (unless I forget) since, well, that’s what some people expect…

Some more reading: here