I searched the meaning of reel in a couple of dictionaries and got the meaning as
to walk, moving from side to side, looking like one is going to fall.
but still I am not able to understand it. What does it mean? Can I have an example in favor of that word?
Psalm 127:27
They reel to and fro, and stagger like a drunken man.
The definitions you found describe how someone who is drunk might walk: not in a straight line, and in danger of falling over.
To reel in terms of walking is not commonly used (Andrew Leach's example is a good one though). What you would more often see: 'He reeled backwards from the punch' or 'The news sent him reeling' -- meaning that he appeared unsteady, as though he was about to fall over.
A reel is a type of dance. In the Highland Reel (http://en.wikipedia.org/wiki/Scottish_highland_dance), the dancers weave side to side and around each other in a way that the definition you provide suggests. Perhaps it comes from the dance, then?
