One of the more popular strains of meme often has to do with a simple line drawing which conveys nonetheless and impactful emotion. In the case of Challenge Accepted, there is a line drawing of a very sure, confident, and smug looking stick person with stick arms crossed in finality.
This meme will often play off other memes or other references to popular culture. It is a shorthand way of outlining different challenges and accepting them. The challenges can be about anything, but they tend to be things that are out of the ordinary or quite drastic.
Along with the black and white stick figure with its arms crossed, there will be the term "Challenge Accepted" somewhere also in the text of the meme.
The more silly or banal the challenge, the more humor comes from saying the phrase "Challenge accepted". This can apply to all sorts of things in life, big and small, meaningful or not. There is a smug sense of finality, of getting the last word, that many people can understand or identify with here.
In fact, so much of memedom involves getting your say or having that final word or phrase punctuate the discussion of whatever it is and put an end to it. Often, these are words or phrases that most people would have a difficult time responding to, either out of confusion regarding what just happened or because the phrase was so powerful.
Notable examples of the Challenge Accepted meme are: "Threesome? Challenge accepted," and "Rainbow colored hair? Challenge accepted."