Physical significance of resolution in image processsing
So the question really is, "what is a pixel?" 

A pixel when you access the data/sample of the image is just a number. The capturing device has generated this data represents the visible area on a particular surface and the color of the pixel represents the light that is falling on that surface. 

Hence, when resolution of the capturing devices is high, you are able to capture equivalent of finder details from the incoming source of light and its' variations. when the same image is brought down to a resolution of say 1/4 which means the resultant new image represents the average color/intensity of that 4x4 window around that point. Hence, the lower resolution more "pixelating effect" do you see. 

There is one more aspect to see here. The details in image also represents the size of the object subject to the scene geometry. So for example, if you capture a shot in camera which has one flower and a leaf, we identify that if the leaf is roughly taking twice as more pixels than flower, then leaf in real life is twice as bigger (from that perspective) than flower. However, when zoomed out, and pointing to the macro scene, the same number of pixels could be occupied by a full tree. So we can find the relative dimension of the object based on their area in the image because image is nothing but a projection of that scene on the canvas. It is possible to know, however, the exact dimension of the object as well if we can apply some known distances on the canvas or if we know the distance of the object from the camera film. 

So in essence, pixel represent the light intensity or the color of the object at a fixed grid on the scene - the finer the resolution - more pixel reprsent the same object in finer details and more information. And, distance between the pixels represents the relative distance between two points on the scene.