I didn't understand the fact that chiral objects are non-superimposable on their mirror images. I mean, if you put your right hand (apparently an achiral object) in front of a mirror, the mirror image will be like your left hand, but, when you make your hand touch the mirror, isn't it superimposable on its mirror image (and hence achiral)? Doesn't that mean that everything is achiral?
if you put your right hand (apparently an achiral object)
No, your right and left hand are both chiral objects, as we will see below.
in front of a mirror, the mirror image will be like your left hand,
but, when you make your hand touch the mirror, isn't it superimposable on its mirror image
No, that mirror image is not superimposable. Just because the bottoms of your right hand and left hand can overlay one another does not make them superimposable. If you could take that 3-dimensional mirror image out of the mirror and place it next to your hands and compare it to your right and left hand, it would look like your left hand. And, just like your real left hand, you couldn't pick the mirror image up and place it next to your right hand, look at them both and say, "they are the same" because, for one thing, the thumbs are on opposite sides. Therefore, they are non-superimposable mirror images.
Your hands are chiral, that is why you need two different leather gloves, one that only fits your right hand, and one that only fits your left hand. If your hands were superimposable, then you would only need one kind of glove and it would fit both hands.
I have to say that when they taught Chiral molecules to me in Chemistry, they always used confusing molecules to demonstrate. The easiest to visualise the mirror symmetry is with spirenes (spiral molecules).
Think of a spiral staircase, it can spiral clockwise, or it can spiral anticlockwise, but if you tried to put one of each in the same space (superimpose them), nobody could climb the stairs !