This is to try and help with an explanation of Pixels and Pixels Per Inch (ppi)

An Explanation of Pixels.

A 12 Million pixel camera is 4000*3000 pixels.
Inside your camera these pixels are divided between Red, Green and Blue pixels (Normally 3Million Red, 6 Million Green, 3 Million Blue). The clever bit inside your camera or your RAW software turns those into 12 million fully coloured pixels.
After the magic of the software each pixel will be one colour from16 Million colours available (minimum!)
From these 12 million pixels the magic of your software will resize the image to go on the web or go to digital projection. So as an example the club’s PDI contains 1920*1200 pixels (2.3 Million pixels). The process of resizing can use different methods but information is thrown away with the reduction in the number of pixels. At this point any setting of Pixels per inch for Print Resolution or Screen Resolution is irrelevant.
There is a lot of debate about the resolution (pixels per inch, ppi) required for printing. There is a number that is often quoted that the minimum should be 300 ppi. However I have read that it takes an expert to differentiate between 300 ppi and 200 ppi printing and an experiment at the club showed an inability of club members to pick out the order of print resolution. Personally I have printed many images at 160 ppi without any adverse comments about resolution.
If we go back to the 12 Mpx camera with 4000 * 3000 px this will give the following print sizes
13.3” * 10” at 300 ppi  (339 * 254 mm)
20” * 15” at 200 ppi  (508 * 381 mm)
25” * 18.75” at 160 ppi  (635 * 476 mm)
Within the preferences of Photoshop you can set the Print Resolution.
If you set this preference to 300 ppi then for a 4000 * 3000 px image it will report back to you within the Print Dialogue Window a print size of 13.3” by 10” depending upon the units you have chosen. So if you chose to print at 100% the image size will be as shown.
If you then decide that print size is not what you want and change the dimensions or the scale then the print resolution in that window will change to reflect the new resolution.
The Print Resolution setting in preferences is an aid to showing the size of the print. Changing it only alters the reported print size at 100% scale in the Print Dialogue Window. It doesn’t do anything else.
Do not throw away your pixels to print, the more the merrier!

Do not confuse ppi with dpi. Dpi is the dots of ink per inch that your printer will put down. The higher the dpi the better your print will be. Some art papers do not benefit from high dpi settings and may remove them from your printer setting menu. It is the gloss or semi gloss papers that usually allow maximum dpi to be used.
For those that enjoy these things there is a belief that the best performance of the printer is obtained when N = dpi/ppi. When N is a whole number the print is at its best.
So for an Epson working at 2880 by 1440
1440dpi/360ppi gives 4 which is a whole number, good
1440dpi/240ppi give 6 which is a whole number, good
1440dpi/300ppi give 4.8 which is not a whole number, bad
However I’ve never noticed an artefact that I could blame on not having N as a whole number. So personally I set the print size to what I want and only worry if the ppi number gets below 160ppi.