Question

What is accommodation in the eye? how are the muscles involved in this process?

Answer 1

"Accomodation" is the name we give to our eyes' ability to change their
focus for different distances. 

Our eye does this by changing the thickness of its lens, making the lens
thicker to see nearer things, and thinner to see distant things.

The lens in the eye is suspended by a circular muscle all around it.
The muscle can pull on the circumference of the lens to make it wider
and thinner, or relax to make it narrower and thicker.

In the modern age of medical miracles that we live in, if the lens of
a person's eye is injured or becomes cloudy, an ophthalmologist can
replace it with an artificial one, and the person can see again !  But then,
the process of accommodation doesn't work any more.  That artificial lens
stays focused at the same distance all the time, and the person needs
glasses for other distances.

I can tell you that it's not really a big deal.  The lenses in BOTH of my eyes
developed "cataracts", and were replaced with artificial lenses. 
I had a choice !  I could have lenses that are good for distance, and wear
glasses for reading.  OR I could choose lenses that are good for reading
and put on glasses to see things in the distance.  I chose lenses for distance. 
I can SEE again, and I put on reading glasses when I'm reading.  

It's really a miracle when you think about it.