Please help me to understand what does a characteristic impedance mean. I am unable to get the exact idea of what does it actually mean and its physical significance.
The characteristic impedance of a transmission line is the ratio of voltage to current in a traveling wave, and arises from Maxwell's Equations as applied to the physical transmission line structure.
For example, if I transmit a short 1-V pulse into a 50-ohm transmission line, I expect that the pulse will travel along as a pulse of 1V, with a current of 0.02 amperes in the region where the pulse lies at any given instant.
Reflections and other problems arise when impedance is not matched; because current and voltage must sum and match in various ways at a boundary, the pulse must be partially reflected to maintain these boundary conditions. The same occurs at an unmatched load (e.g. if your 1-V, 0.02-ampere pulse hits a 100-ohm lumped impedance, it cannot be totally absorbed since 1/100 != 0.02, and thus some of the pulse must be reflected.
Think of waves in a pool. Waves in water travel smoothly but if material changes like there is a wall then they get reflected back. Transmission lines are similar. As the voltage wave travels for some time in transmission line it looks like a certain impedance, and if the transmission line is not terminated with that impedance then voltage wave gets reflected back. Same when sending voltage into transmission line, it looks like characteristic impedance until the voltage wave has travelled to the other end and sees termination, so therefore transmission lines are usually driven with characteristic impedance as well.
One fact about characteristic impedance that helped me understand it: If you measure the impedance "looking down" an infinite length of transmission line, you will get the characteristic impedance. That is, measure the impedance across the terminals at the end. (If you are tempted ask whether it's open or closed at the far end: In the limit as the line is infinitely long, it ceases to matter.)
This goes hand-in-hand with the fact that, if you want to prevent reflections at the end of a transmission line, you terminate it with a resistor equal to its characteristic impedance. You should be able to see that, if an infinite length of transmission line has impedance Z, then you should be able to cut it at any point along the length and replace it with an impedance of Z across the line (which will be a termination resistor, if Z is purely resistive), and it should "look" as though there's still an infinite line attached, so the wave won't reflect.