Hope you folks don't mind if I expand on this topic. If nothing else, it will help me cement my ideas. So here goes:
Image size depends upon two things: The number of pixels and the size of the pixels. Of course, this is two dimensional. We have image height and image width. If you want to we can express actual image dimensions as two equations -
Image Width = Number of pixels wide * Width of pixels
Image Height = Number of pixels high * Height of pixels
For this discussion, we can assume that pixels are square and so pixel width = pixel height.
In Photoshop, you can independently set any two of the three elements in the above equations and Photoshop will calculate the third. When intending to print an image I find it helpful to think about the right hand side of the equation first - particularly the size of the pixels.
Pixel size
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You measure pixel size by seeing how many will fit in a straight line in one inch. This is the unit "pixels per inch". More commonly, the term "dots per inch" is used but this is not accurate as the two units are not necessarily equivalent - we'll see this when we talk about printers later. For now though, pretend there's no difference.
Pixel size is what most people are talking about when they discuss "Resolution". If you look at an image in photoshop and zoom the image to 400%, you'll see the image made up of little squares. These are the pixels. Mostly, when you print an image, you'd rather not see the pixels when you look at the print. Seeing the pixels depends both on their size and how far away you are from the print when you look at the image.
If you have a very large, say wall sized, print on a billboard somewhere and you stand on the other side of the road, the pixels would need to be very large indeed before you'd actually be aware of them. Cross the road and take a closer look and you'll find that they are easy to see - but now you can't see the full picture because you're too close.
When you are thinking about printing an image, the first thing to think about is how big the pixels should be - and we can figure this out by determining how far away from the print you'd like people to be when they view the image. By and large this translates into how big the print is going to be. Big prints are designed to be viewed from further away than small prints. A rule of thumb is "viewing distance = diagonal of print".
The human eye is such that at about 15 inches viewing distance it's very hard to see pixels printed at 200 ppi. If the image contains high contrast diagonals like printed text, you might just be aware of "jaggies" - the rough edge caused by trying to create a diagonal by joining tiny squares. In this case 300 ppi might be a better option. 15 inches is roughly the "normal" viewing distance for an 8 x 10 print. Personally, I think these numbers apply to people with super-vision like people from the Kalahari! Suffice to say that if you print an 8 x 10 at 300 ppi you won't see the pixels.
If you now want to print a 16 x 20 and consequently have it viewed from a further distance, you could get away with 150ppi pixel size.
So now, let's say we've chosen our required pixel size - 200 ppi. To set this for the image in Photoshop:-
Image -> Image Size
Make sure that the check box marked "Resample Image:" is NOT CHECKED. The pixel dimesions at the top of the window will now be disabled - meaning you can't change the number of pixels in the image.
Now type 200 into the "Resolution" box and set the unit to "pixels/inch".
Click OK
You have just changed the size of the pixels. The number of pixels is still the same. The size of the image will be different (refer back to the equations at the start for why).
Number of Pixels
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You might have found that for the image in the above example, the image width is now 12". But you want the image to print at 16" x 20". You have 4" to go. How do you fill in that 4" of space without changing the pixel size which we just so painstakingly decided upon?
We're going to have to add more pixels! The gurus amonst us have worked out various mathematical incantations to add pixels to an image based on the pixels that are already there. They do this in such a way as to minimise any perceived degradation in image quality. People will recommend all sorts of approaches here. Using other software. Using Photoshop but adding pixels in small stages etc.. etc... You can read all about that elsewhere. For the purposes of this discussion, we'll just use Photoshop's "bicubic" algorithm and we'll do it in a single step.
Image -> Image Size
Make sure that the check box marked "Resample Image:" is CHECKED and that the drop-down box reads "bicubic". The pixel dimesions at the top of the window will now appear enabled - you could change the number of pixels by typing in here - but we won't.
Make sure that the check box marked "Constrain Proportions" is CHECKED. This keeps the width/height ratio the same if we change one of them.
Now type 16 into the "Width" box and set the unit to "inches". Note that the number of pixels just increased. Also the height of the image increased. We'll just assume for now that the image has the correct proportions for a 16 x 20 print and so the height reads 20 inches.
Click OK
Photoshop takes a little longer with this operation because it is busily calculating what new pixels it should add where. When it's finished, you have a 16" x 20" image with a pixel size of 200 ppi. You're ready to print it (on your large format printer, of course...)
Printer Resolution
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Printers, that is, ink-jet printers, spray tiny dots of ink onto the paper to produce an image. Modern printers can actually vary the size of these dots. So you can have printers with "1440 dpi resolution" meaning that they can fit 1440 dots into an inch. This is very similar to the pixels per inch of the image. There is a common misconception that you have to match the image resolution to the printer resolution. In this case that would mean we'd want the image to have a pixel size of 1440 ppi!! Wrong! We just spent ages arriving at our nice 200 ppi pixel size for very good reasons. Let's not destroy that work and also end up with an enormous image file size by trying to perform this match!!
Printer resolution simply allows the printer to use more dots in painting a pixel onto the paper. While doing this, it is also performing some mathematical magic to make the colour transitions from one pixel to the next very smooth. This results in very high quality images.
When you print, your image prints at 200 ppi. The printer can be set to 720 or 1440 dpi or some other setting. And that's just fine. 
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Wow! That was an essay and a half! Anyhow, that's what I think I've learned in my reading and using to date. If I've stuffed up, PLEASE TELL ME!
Sorry it was so long...
