It comes up fairly frequently and the confusion is usually regular, so this brief tutorial is going to be about PPI and DPI, pixels per inch and dots per inch respectively. PPI is used in two contexts, to describe the resolution of a device such as a computer monitor or a scanner or it can be used to describe the resolution of an image to be printed. As such PPI doesn't actually refer to the physical dimensions of an image, only how many pixels there would be in any given inch.

The confusion arises between PPI and DPI as computer screens are often referred to having a resolution in dots per inch, when in reality the resolution is actually measured in pixels per inch. DPI is more accurately used in printing, which I’ll describe below. A computer monitors PPI can be calculated by taking the one of the dimensions as measured in pixels and dividing this by the related physical dimension (so a monitor that has 1920 pixels on the long side and is 23.5” wide has a PPI of just under 82 PPI.

The really confusing aspect of the PPI is when someone is asked for a particular PPI in their image. For example the Veolia wildlife awards require an initial submission with images that are resized to 1920 pixels on the long side and are set at 300 PPI. An image that is 1920 pixels wide at 300 PPI is identical in every respect to an image that is 1920 pixels on the long side but set to 72 PPI. The digital resolution is the number of pixels. The PPI is how those pixels are going to be translated onto paper. Here more pixels per inch means for better quality.      
There is a caveat though. The human eye resolves detail between 200 to 300 PPI. Anything less than 200 PPI and we are likely to start seeing loss of detail. Higher than 300 PPI and the gains in detail are practically academic as we are unlikely to see much difference except under a magnifying glass (some print houses now have new machines that print at 400 PPI - theoretically images look crisper and sharper, but good post-production and effective use of sharpening would have the same perceptual result).

The important thing to remember is that one pixel is not the same as one printer dot. Printers can spew ink onto paper at a great many times more dots per inch than the digital resolution of the image. They do this so that more accurate colour can be put down on paper by layering dots in a small area. My Epson printer is able to print at 2880dpi. What that means effectively is that there are 2880 printer dots in an inch but that the digital resolution might only be 300 pixels per inch (so 9.6 printer dots to each pixel). The greater the dpi the better the colour rendition on the print, but it is not related to the resolution of the image.

Another confusing aspect is that the paper resolution of an image is not the same as digital resolution. This is already demonstrated by the fact that a 2000 pixel wide image is going to remain a 2000 pixel image regardless of the ppi that is tagged to the file (and the file size won’t change either). But viewing on a screen is going to be very different to viewing it on paper. Try this: resize an image to something relatively small at 300 PPI. Then take a ruler and view it at 100% on the screen. The ruler setting and the print resolution indicated in resize dialogue are going to be very different. There are programs that replicate the size of the paper on screen.

So  why do we need to know about PPI and DPI? It’s important to know what we are talking about when we finally get round to printing our images. Resolution in the image resize dialogue in Photoshop is actually the printing size. If we disable the ‘Resample Image’ box near the bottom of the box, we change the physical size of the printed image without changing the actual number of pixels. If the Resize image is ticked, Photoshop will either remove pixels or create new pixels (it does this by interpolating the image—basically inventing new pixels based on existing pixels).

On screen the computer actually ignores the dpi value that is embedded in the EXIF data of the image. If an image is sized to 480 pixels on the long side, you will see 480 pixels (some people in the print industry use the 72dpi value in order to approximate what the image would look like sized on paper as Apple screens started the trend of having pixels that were sized at 72ppi,  PCs differed slightly with a published ppi of 96).

As a basic guide to printing, rather than inventing pixels with the resize command, change the ‘resolution’ with the Resize Image switched off. Printing industry standard may 300ppi, but when printing it is possible to go down to 200ppi without any perceptible loss of acuity (Scott Kelby and Adobe seem to be on a crusade to change this perception by setting defaults to 240ppi rather than 300ppi).  Otherwise follow guidelines when submitting images to libraries and competitions. They ask for 300ppi as they want to know that the image has enough information to print at 300ppi. It’s just easier to look at the EXIF data of hundreds of images  and see the little ‘300’ rather than looking at the actual pixel count that gives the image’s digital resolution.