I understand pixels per inch but I don't understand how they are displayed on a monitor. ...

In other words, the number of pixels per inch on the monitor doesn't change, so are the larger pixels in the graphic actually displayed by multiple pixels on the monitor?

yes

By default, Gimp sets one image pixel to correspond with one monitor pixel.

This is a setting in menu: View -> Dot for Dot -> either or off

This screen shot (Gimp in multi window mode to compare images) 2 images, both 300x300 pixels, both 100% zoom but 1one is 100 ppi and the other is set 300 ppi. As you expect, both are the same size on the monitor.

http://imgur.com/V7rcAbp

If I turn Dot for Dot off then the images show at their true resolution, still 300x300 pix, 100% zoom but one is 3 times the size of the other corresponding to their ppi setting.

http://imgur.com/UM0rCga

Providing the monitor resolution is correctly set Edit -> Preferences -> Display then this is the size the images will print.

Obviously for editing, better to have Dot for Dot on.

other words, the number of pixels per inch on the monitor doesn't change, so are the larger pixels in the graphic actually displayed by multiple pixels on the monitor?

That still did not explain it very well. To get your image with one 'clean' circle, one 'pixelated' circle, side by side, the pixelated circle must have been scaled up by N. One pixel is no longer one pixel, it is 1 x N pixels, according to the scaling factor.

Thanks, I understand that, but what I'm curious about is whether the larger "display" of a pixel is represented on the monitor by numerous pixels...Because the display has a fixed number... So for instance, my monitor is set at 1600 X 1200 but if I display an image that is like, 20 ppi does the monitor use multiple pixels to display each pixel in the image?

Yes

but...You are ignoring the gimp scale factor that might be in place.

With dot-for-dot on one screen pixel maps to one image pixel **at 100% zoom** This screenshot with screen rulers which measure screen pixels. Left image 400x400 @ 100 ppi Right image 80x80 @ 20 ppi. That is what they measure **at 100%** 400 pix and 80 pix

http://imgur.com/O90wHiy

Again dot-for-dot on, If the 80x80 image is zoomed in 500% then obviously they appear the same size on the screen. Gimp has interpolated each single pixel in the image to 5 pix on the screen.

http://imgur.com/ZmNTvR6

The other view is with dot-for-dot off and both images at 100% zoom. In this case Gimp shows the images as they will print and for the 80x80 image again Gimp interpolates each image pixel to 5 screen pixels.

http://imgur.com/I0uBHSU

None of these change the number of pixels in the image. For normal Gimp editing Gimp will interpolate image pixels for the display.