When people create designs for the web (viewing on screen only), we can usually suffice with 72dpi. If we calculate the resolution of a fairly dated 15″ 1024×768 monitor, that works out to 68dpi, whereas a more modern 1440×900 15″ MacBook Pro display would work out to 96dpi. As monitor sizes and resolutions increase they will be capable of displaying much higher quality imagery, but for now 72dpi seems to be the rule of thumb.
If you created a document at 72dpi that you then wanted to be 300dpi you would not simply be able to change this because you can’t generate the extra pixels you require. You would have to start from scratch and recreate the design from the beginning with the file set to 300.dpi at the start.
If you did change the resolution from 72dpi to 300dpi, Photoshop would guess what colour pixels to insert, but as you can imagine the end product isn’t going to look too good. This is known as Resampling. You can change a 72dpi image file into a 300dpi file by resizing. This is when Photoshop takes the number of pixels it has to play with and divides them up so that there’s 300 pixels in every inch instead of 72.