Explain this common observation clearly: if you look out the window of a fast-moving train, the nearby trees, houses etc. seem to move rapidly in the direction opposite to the train motion, but the distant objects seem to be stationary.

Hint: there is a very important concept of relative velocity that when you watch any object with respect to a moving frame of reference then you have to add a velocity vector(to the velocity of body which you are observing) of same magnitude and in opposite direction of your own velocity for example when you see a standing man on rod from your moving car that seems to be coming towards you with the same velocity as your car but in opposite direction.

Complete answer:
When we see object it is clear from the relative velocity concept that both the nearby and the distant object move in backward direction but there is an illusion created due to which the nearby trees, houses etc. seem to move rapidly in the direction opposite to the train motion, but the distant objects seem to be stationary. This thing is happening because the angle between nearby objects and eyes(retina) changes more rapidly than the distant objects. Also, when you look distant object then you compare their velocity relative to nearby object because nearby objects come between you and the distant objects when you compare the velocity of distant object with respect to nearby object that seems to be move forward relative to nearby object so that is the main reason why this illusion is created and distant object seems to move forward with respect to you.

Note:
Use relative velocity concept to find the velocity of other objects with respect to you. In this question if somehow you are able to avoid the nearby object and only see distant objects with your eyes then the distant objects are also moving in backward direction with respect to you.so the best way to save yourself from this illusion is to avoid nearby objects somehow. If this illusion is correct then the distant object travels with you and as you travel from Delhi to Bombay they also move with you but hopefully this is just an illusion and not true in daily life.