Herp Derp is an internet "meme" indicating stupidity or randomness. A lot of people think it's pointed to insult retarded people but it's not. When used seperately, Herp and Derp become "anonymous" names to use in those internet meme comics called "Rage Comics". Herpina and Derpina are the female alternatives.
"Ugh I'm such a derp, I forgot to do a water change"
"I PUT MY BETTA IN A 0.25 GAL TANK HERP DERP HERP DERP" (Trolling)
"Hey Derpina do you want to out to see a movie tonight?"
"Sorry Herp, I'm busy >_>"
Herp Derp is also used in images where somebody makes a really funny, unnatural looking facial expression.