Sorry if this is teaching you to suck eggs....
An image contains a certain number of pixels, x by y, so long as you don't upsample (expand the image and create extra pixels) or downsample (condense the image into fewer pixels).
The resolution is simply a factor of the number of pixels in the image divided by the size you choose the image to be displayed or printed at. Or, equally, the size of the images is simply how many pixels it contains divided by the resolution you set.
On screen, if you zoom in or out you change the resolution. So by setting the resolution for display on screen you simply define how big it will be displayed but as soon as you change the size (by dragging a bounding box or zooming in, etc) you also change the resolution - but it has no effect on the content of the image.
Equally if you print (without resampling) at different sizes you end up with different resolution prints.
However, the "resolution" tick box in the Lightroom Print module is actually an instruction to resample your image. So it will either create extra pixels to print or condense the image into fewer pixels. To maintain the relationship described above you need to untick this box completely. If you then tick the dimensions box higher up, the true resolution of your image will be displayed top left.
This resampling by lightroom is only done "on the fly" whilst making the print so it still would have no effect on your master image, just on what the print would look like (usually a positive effect but this is another lesson - check out the lightroom video tutorials or "From camera to print" video tutorial).
Hope that helps.