What's shown
The image is a large head with wide outlines, drawn in this variant with a bold line. The eyes look in different directions: one points sideways, the other upward, the pupils are lowered, and the eyelids look half-closed. The mouth is stretched into a crooked grin, out of which the tongue hangs.
The overall impression is a carefree but clearly unintelligent face. The image needs no context: the facial expression alone makes it clear that the character either doesn't understand what's going on or is proud of not understanding anything.
In the original comics such faces were drawn together with a body, but what entered meme usage was mainly the head, because it's the face that carries the meaning. The female variant, known as Derpina, is distinguished by a bow in the hair, while the basic expression stays the same.
Origin
The word "derp" means witlessness or foolish behavior and spread through American English slang. Its specific history hasn't been precisely established: sources don't say who first used it in its current sense. The face became a meme already within rage comics, when the word acquired a visual image.
The earliest documented appearance of the face is tied to the comic "Rage Comic FFUU," which user ULJarad submitted to the subreddit f7u12 on May 11, 2010. In this comic the face is drawn deliberately clumsily, and the text itself mocks bad drawing. As early as October 11, 2010, a post titled "Harp Darp poop on my car" appeared on Reddit, where the same face was used in a joke about bird droppings on a car.
The variant "Harp Darp," or "Herp Derp," caught on as a standalone name. It was under this tag that the meme spread across FunnyJunk, Tumblr, and Memebase. The same expression lived under different names, while the overall meaning stayed the same.
Derpina and the female image
The name Derpina, judging by the sources, was formed from the male variant Derp, and the female character had appeared in rage comics since 2010. The earliest documented use dates to February 9, 2011, when a mention of this character appeared in the "Memes of 4chan" thread on the PokerStrategy forum.
In February 2011, comics with Derpina appeared on Tumblr and FunnyJunk, in March on Memebase, and in June 2011 she got an Urban Dictionary entry and her first Facebook page. By January 2013 the page had gathered around twenty-two thousand likes. A Spanish-language page, created in January 2012, gathered almost forty-five thousand within a year.
The distinguishing feature of the female image became the bow in the hair, which helped tell the character apart from the male variant. Fan drawings on DeviantArt in early 2013 numbered more than a thousand works, which shows how widely the image was taken up by creators.
Spread
The face quickly grew its own infrastructure. On April 12, 2011, the site HarpDarp.com was registered, which showed only this face. On April 22 of that year, the first Urban Dictionary definition appeared: "an exclamation after an instance of top-tier stupidity."
The image also moved offline: in November, an artist selling on Etsy produced hand-carved stamps with this face. Around the same time the meme began to be used in chats and comics, and the tag "herp derp" united dozens of works across different platforms.
On January 18, 2012, web developer Tanner Stokes released a Firefox extension that turned YouTube comments into sequences of "herp derp." Similar tools for Chrome, Safari, and Opera appeared in July 2012, which shows how widely the image became internet slang.
Use and reasons for success
The meme's typical function is to flag someone's stupidity, a nonsensical statement, or a careless remark. The face is placed under text that looks senseless, and the reader immediately gets the irony. That's why in rage comics it was a convenient shorthand instead of a long explanation.
A second use is as a filler. "Herp derp" is used in place of a word one can't recall, similar to "thingamajig" or "whatchamacallit." That's how the meme entered colloquial speech and became a joke about one's own absent-mindedness.
The image works because its expression is easy to read and requires no knowledge of context. The meme mocks stereotypical stupidity rather than a specific person, so it remains harmless at its core, though not always flattering to those teased with it.