What is character? what is the
exact definitation of it? How can one judge on
this parameter so as to improve?

Character is the sum total of the responses expected of us in various situations. Its a reflection of the inner being that we are. All good men are men of Character. We call them good for they responded to their situations in a way that is universally accepted as right. By universal acceptance I mean across cultures and religions there are a few things that are considered to be right or good.
Talking of Character one cannot forget what Swami often stresses 'End of Education is character'. I feel this defines what an education is supposed to do and what can be called as true education. If the education helps one to be of good behaviour then its truly 'education' or else its just transfer of 'information'.
The society, company and family that we are brought up define our knowledge of good and bad and decide our character. 'Tell me your company and I shall you what you are' explains the importance of our friends and surroundings.
To improve our character few ways could be
-To see the way the people whom we take as role models behave in a particular situation, and emulate them. This needs us to look for an individual whom we admire. Reading of the stories of God or life stories of great personage like Mother Teresa, M.K.Gandhi, Aurobindo et al. helps us build our ideas of good actions. Here one is reminded of Swami saying that we should thing first of God, then world and last ourselves. For this was what differentiated the Pandavas from the Kauravas w.r.t. their priorities in life. Any action we do should be acceptable to God and do good for the society. If these two are taken care of, then we will be 'taken care'. A simple way suggested by Robin Sharma is when you do any action think if you would be happy relating it your mother. I feel this is very practical. For Mother has the purest form of love possible.
-always give yourself sometime to think before taking up any new action and not act in a hurry or in a mob mentality.
-At the end of the day we should try to recollect the times we have not followed what we felt was right but gave in to the pressures of the surroundings.