The following two photos of the classroom were taken from the same spot with the same camera, and as such appear nearly identical. The one on the left, however, was taken at a setting of 4272 x 2848 pixels, and the one on the right is 1920 x 1080 pixels.
On a monitor, this is of no real consequence. The real benefit comes into play when one of two things happens:
If I needed only a very small portion of the photo above, say part of the power supply cables, I would crop down to that specific portion and then re-size that part of the image if necessary. Since it was at such a high resolution, the photo on the left can clearly represent the cables at 100% zoom on a screen, while the one on the right must be resized significantly to take up the same space on a display. The results are seen below:
So, it's very easy to see that higher-quality photographs offer you a huge benefit when you only need a portion of the image, or need to do some cropping to remove unwanted elements or better compose the photograph.