Dispelling the myths about pixels per inch and resolution
A common misconception that most people have is that the pixels per inch (PPI) or dots per inch (DPI) of an image has some bearing on the quality of an image. The truth of the matter is that pixels per inch is more like a meta data tag that tells printers how big you'd like an image to be printed.
Resolution and pixels per inch are often confused with each other. In terms of image quality ppi does not equal resolution or quality at all. The resolution of an image is the total amount of pixels it is made up of. For example 3,000 horizontal pixels multiplied by 2,400 horizontal pixels equals 7,200,000 pixels, or 7 megapixels. Where as the pixels per inch value is simply telling a printer or photo viewer how many of those pixels should be displayed per inch of paper of screen space.
So why do people confuse pixels per inch with resolution? The term pixels per inch is also (more suitably) used when describing the resolution of screens. For example a 27 inch iMac with Retina Display has 218 pixels per inch, and an iPhone 6 is even higher at 326 pixels per inch. But this shouldn't be confused with the pixels per inch of an image.
With that cleared up, here is how to change the PPI of any image should you need to:
Open your image in Photoshop and go to Image > Image Size..
Deselect the Resample option if it is checked. Enter a new value in the Resolution* field and click OK.
It really is that simple! You now have an image of the exact same quality and resolution, but the pixels per inch is now 300 instead of 72.
*Thanks Photoshop for adding to the confusion between pixels per inch and resolution.