In the middle of swapping front brakes, I was examining the caliper piston as someone told me check it for free movement. I didn't fully understand what free movement for a caliper piston was like. Should I be able to pull out and push in the caliper pistons with bare hand if it is normal and not binding?

 

press the brake lever and watch the pistons come out .. if they come out smoothly that is what they mean ..
generally you dont have to do that.. if you had a piston hanging up you would know it a long time ago .. the bike would have pulled to one side..

or when you take the pads off the front rim one side would be worn ALOT more then the other