Question

Though we say image is formed at same side of concave mirror we can see image in mirror how and why

Answer 1

you are right about following things:

1. Concave mirror forms an inverted, real image in front of it (for the case of object being far from focal length of mirror)
2. Real image is can be obtained only on a screen

Now add following fact to it:

1. Human eyes see by forming a real image of objects on the retina
2. Human eye can (re)focus to see anything kept farther from minimum distance of vision (which is assumed to be 25 cm for a normal healthy eye)
3. Human eye when viewing through another optical element behaves as a cascaded optical imaging system (i.e. like many lenses, mirrors together)

Okay, now we are well equipped to answer why can you see real image through concave mirrors:

1. The real image of objects (generally placed very far away from mirror) is formed closer to the focal length of concave mirror
2. When we look into the mirror, we are farther than the focal length of mirror, thus our eyes tries to image the real image formed by mirror (it is inception style thing ...... forming image of another image ...... but that is exactly how you analyse a multiple element optical system.

So, what we see is an image of real image formed by the mirror. If you want to confirm it here is a small experiment for you:

1. Take a shiny spoon
2. Use the concave surface of the spoon to look at objects, you can clearly see them ? Right? That is exactly why you asked the question.
3. Now, what happens as you move the spoon closer to your eye (keep the spoon slightly tilted so you can still follow the image formed) ..... you will notice that at some point the image will go blurry! This is the point where your eyes are at their minimum distance of vision away from real image formed by the spoon. If you go to the plane where real image is formed, you will not be able to see anything