The real-world reason for this was because of the makeup constraints of 1960's technology. However, an in-universe explanation for this was developed in Enterprise; a good summary of it can be found at Memory Alpha's page for the Klingon augment virus.
It is a long story.
The Klingons in TOS have no ridges due to the augment virus as stated above. The real world answer is related to the fact when the original show was made there were very few networks willing to show black actors on television thus the caucassian actors of the day regularly appeared in "black face".