Something that makes absolutely no sense in the context of a sentence, story, TV show, book, play or movie. Alternatively, something that is incredibly out of place.
This term originated from Cleolinda Jones' LiveJournal recaps of the television show Lost. In one of the early episodes, the characters come across a vicious polar bear in the middle of the jungle. This animal was so out of place and out of context that in her recap, Cleolinda referred to it as the "OMGWTFPOLARBEAR".
Person 1: What is a My Little Pony doing in the middle of an action shot in Transformers?
Person 2: OMGWTFPOLARBEAR!?