Easily the most important sentence in
Linguistic-
Cognitive Science.
Comes from a series of debates between Chomsky (a linguist) and Skinner (yes, the Behaviorist with the rats we all know and love) over the nature of language.
Skinner wanted to say that language is a sort of chain, and that we are conditioned to expect certain words in sequence. Say, after 'stop', we expect words like 'watch', 'there', 'light', 'time', and others. He said that's how we learn language; it's conditioned just like everything else in his theory, by exposure and repetition.
To refute this, Chomsky composed the sentence 'Colorless green ideas sleep furiously.' It is a sentence that is semantically correct (in that it violates no 'rules' of language, ie, no dangling participles, etc) but makes no logical sense. In addition, each pair of words, 'colorless' and 'green', 'ideas' and 'sleep', 'sleep' and 'furiously', you had probably never heard them paired up before. And yet, in a certain way, the sentence makes sense.
So, even though you've never heard the sentence before, and probably never heard those connections of words, the sentence makes some sort of sense. This violates completely the Behaviorist-Conditioned Response view that Skinner was trying to put forward. He was stumped, and had no real response, nor did his colleagues.
On a side note, there is apparently a yearly contest to write something that makes the phrase make sense. Of course, the descriptions given would likely never happen, but that's the point of it. Even though you've never been exposed to it (given the appropriate stimulus) you can still make sense of it (response).