The cause revealed
In February 2005 a two-part storyline on Star Trek: Enterprise, "Affliction" and "Divergence", explained canonically why the Klingons changed their appearance.
In an earlier series of episodes, the Augments, humans grown from genetically engineered embryos from the Eugenics Wars of the late 20th century, were defeated by Captain Jonathan Archer and the Enterprise NX-01 in Klingon space. The Klingon High Council feared that Starfleet was developing armies of Augments and that they would pose a serious threat to the Empire's existence. Even when they were told by the Vulcan High Command that the Augments were created without Starfleet's knowledge or consent, they remained suspicious and so decided to fight fire with fire. The Klingons gained access to the genetic material of the human Augments, and wanted to adapt this genetic engineering to augment their own species. The experiment did not work correctly; at first, subjects did gain increased strength and intelligence, but their nervous systems could not handle the strain and they died. One of the test subjects had a virulent flu, which — combined with the genetic changes wrought by the experiment — became a deadly, airborne plague that spread rampantly across the Empire, from world to world, causing the physical changes to change them into the human-looking Klingons of Kirk's day.
Dr. Phlox of the Enterprise NX-01 formulated a cure for the virus, however not before millions of Klingons were physically altered. And owing to the genetic nature of the virus, these alterations were passed to succeeding generations of offspring.
The Klingons were apparently so embarrassed by the fallout from this disaster, that they absolutely refused under any circumstances to discuss the incident with outsiders in later years. There is also evidence (illustrated by the ignorance of members of the Deep Space Nine crew who encounter humanlike Klingons during time travel into the past in Trials and Tribble-ations) that knowledge of the change might become lost over time to mankind. The Enterprise storyline also indicates that an early form of the Starfleet intelligence service Section 31 was somehow involved in the transformation of the Klingons.
Phlox indicated that "someday" the physical alterations could be reversed.
The episode "Divergence" revealed that not all Klingons were affected by the virus. No canon explanation has yet been offered to suggest why only the humanlike Klingons were seen in The Original Series, save for statements made in "Divergence" that the genetically altered version of the race would be stronger and more intelligent, suggesting they may have been desirable soldiers in later Klingon/Federation conflicts. The Klingons in Star Trek: The Motion Picture were the first Klingon crew that was shown to be dealing with something other than the Federation, so there is no evidence proving these particular Klingons had ever been afflicted. Other possible explanations include the idea that by the time the cure to the virus had been administered to all Klingons, every last one was infected by the virus so that they would have been changed somewhat by the virus anyway. This could also explain the "darker-skinned" Klingon observation stated above. The darker Klingons could have been descendants of Klingons that had only been in the initial stages of alteration when they were cured, so that they retained their more natural pigmentation. It is also possible that some Klingons used cosmetic surgery to restore their pre-alteration appearance.
However, the ridge-development cure must have been developed before 2293, the year of Star Trek VI: The Undiscovered Country. The Star Trek: Voyager episode "Flashback", which depicts events that took place in 2293, shows the Klingon Kang with ridges, though he had none in the original series episode "Day of the Dove."
It can be calculated, therefore, that the humanlike appearance of the Klingons lasted for at least 119 years, since these two episodes of Enterprise took place in 2154, and the reversal mentioned by Phlox could have happened before Star Trek: The Motion Picture which takes place in 2273, but had definitely happened by 2293.
In the Star Trek: Vanguard novel Summon the Thunder, the humanlike Klingons are called QuchHa', or the unhappy ones. They usually serve in their own units, although sometimes they are known to mix with the rest of the fleet personnel.
All attempts at retconning aside, the changes in Klingon appearance can best be explained by an inconsistent treatment of pre-existing material by the series' and movies' writers. Fans have followed several variations of both canon and non-canon sources to produce Klingons with varied fusions, mixtures and heritages. These are portrayed in fiction, fan-produced films, and in professional fiction, such as The Final Reflection and How Much for Just the Planet by John M. Ford and Kahless by Michael Jan Friedman.
LOL pure nutters tbh
