I am sure this is a simple question, but the answers I have received from people are never simple. I am trying to apply an answer to this question for scaling images for the iOS Retina display.
ppi = pixels per inch = typically used as a measurement for screens (the iPhone 4 has twice the ppi as the iphone 3)
dpi = dots per inch = typically used as a print measurement and refers to the number of pixels in the image that will be used to render 1" on paper
scaling = this is a loaded term and why the answer isn't simple. For raster images, you can scale an image a number of ways in Photoshop. Some of these ways may change the ppi settings. Some of these may change the actual number of pixels.
All that said, for working with screen graphics, discard the whole concept of ppi and dpi for your own images. All that matters are your image's pixel dimensions.
If you have an icon that is 100px x 100px and want to make a crisper, retina display version, then that version of the image would need to be 200px x 200px.
So, technically, an image that will be displayed at the same physical size on an iPhone 4 as the iPhone 3 version appears would have to have 4 times the number of pixels, as each axis of the image now is twice the pixel dimensions.