What exactly is Characteristic impedence in transmission lines?
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.