I'm sure most of you know this phrase, what does it mean? Does it represent stupidity cutey thing that they do? What makes this phrase so popular?
I don't think that it is of japanese origin though.
Teehee is just a cute giggle, pretty common internet slang. More on it can be found at the Urban Dictionary, mainly
The sound of a giggle. Used by (1) schoolgirls and (2) old geezers pretending to be schoolgirls.
Defintion: 1)The act of joyful giggling. 2)A noise made to convey happiness 3)Presented to imply innocence
The head punching and tongue sticking out makes me think the "teehee" is a translation of てへぺろ ("tehepero"), which has a literal meaning of "teehee tongue-sticking-out". It actually has a recent history as a word in its own right: this blog post and this crunchyroll news article have some information about it.
Basically, it's the word that goes with teehee+punching head+tongue sticking out, and the meaning is primarily focused on definition 3) that Omega posted - it sweeps under the rug a mistake or ignorance of the speaker with a playful gesture. A Japanese source for this meaning is this scan of an article about tehepero being Japanese neologism of the year, although the expression is likely related to peko-chan (see What is the origin of this facial expression with one's tongue sticking out?).