[HTC One X] knoxploration:
You're welcome, and apologies if my reply seemed grouchy, I'm just shattered today, couple of late work nights in a row does me in.

A good analogy, it oversimplifies rather but should make it really easy to understand:

* Imagine you have a brick wall, made out of square bricks stacked in vertical columns. Each brick is one 'pixel' (ie. dot) on your LCD panel, in your printed photo, whatever. This is your output resolution.

* Imagine you are going to paint a mural on the wall, comprised of square 'pixels'. This is the image from your camera.

* You can paint the 'pixels' from your camera at any size you like. You could paint one pixel on every brick (aka a 1:1 display), you could paint grids of ten by ten pixels on every brick, or you could paint each pixel on a group of ten by ten adjacent bricks. Or any other size you feel like painting it at, honestly. It doesn't even have to match--you could paint every pixel across 1.37549 by 1.37549 bricks, if it floated your boat. ;-)

* The only difference caused by painting your image across more bricks is that if you stand in the same place, the picture will appear bigger and blurrier / less detailed, or smaller and sharper / more detailed. Or, you could paint the picture bigger and then step backwards to view it from further away, or vice versa, and the picture would look identical to your eyes. You'd simply be changing the ideal viewing distance.

* Now imagine the bricks are translucent, and you shine a light on the wall you just painted, then go stand on the other side of the wall. Each brick would be lit up the color you painted, and if your painted pixels were smaller than the bricks, or overlapped partial adjacent bricks, then the bricks with more than one color wouldn't show multiple colors. They'd show one color that was the average of the different colors painted on their other side. (ie. if half the brick was painted black, and half white, on the other side that brick would simply look gray.) This, incidentally, *can* make pictures look a bit soft; if the pixel grid doesn't match the brick grid because your pixels are larger than the bricks (but not an exact multiple of the brick size) and there are bricks that are showing the average of multiple pixels, that reduces the detail you're seeing when you stand on the other side of the wall, and makes the picture look softer. That's why you want a touch of unsharp mask if you upscale (interpolate) an image to make it bigger than the original. It's also why digital zoom is crap; you're basically just seeing the same data spread across more bricks, and your camera is guessing what color those bricks should be. If your pixels are smaller than the bricks, you're basically throwing away detail. That's why you if you shrink (downsample) your image, then upscale it again, you'll get a blurrier image. You've thrown away data that you can never get back once you shrank the image, in a non-vector format.

* All the 'dpi' figure in the EXIF header of an image does is tell the artist painting the image that he or she should scale the image to a particular size before painting it on the wall. The wall itself won't change; the number of bricks is the same regardless. Nor will your image change; the artist would still paint the same number of pixels. Nor would painting the image on a different wall that had bigger or smaller bricks make any difference; there would still be just as many pixels, they'd just cover more or less bricks per pixel. The difference is merely that you're telling the artist what size you'd like him or her to print the image at, in a slightly obtuse way. Instead of saying "Paint me an image four feet across", you'd be saying "Paint me an image where every pixel is six inches wide, regardless of how big or small the bricks in the wall are." He or she still has just as many pixels to paint to finish the mural, and your instruction would just dictate the overall size of the image precisely. If you wanted the artist to paint the image bigger or smaller, that instruction would have to be ignored.

And that, in a ridiculously detailed and yet somewhat oversimplified nutshell is what dpi's about.