First coined by Miriam Weizenbaum, the daughter of a friend of American philosopher Daniel Dennett, the word describes a phrase or statement that is appears profound but is actually asserting a triviality on one level and something intriguing but false on another. Dennett first used it at his 2009 speech to the American Atheists conference. A deepity will have at least 2 meanings built into it, one that is trivially or superficially true, the other that on the face of it seems profound but in reality would be earth-shattering if actually accurate. The example that Dennett gave in his speech was "Love is just a word". This is superficially true, linguistically "love" is indeed just a word, but the secondary thought-provoking meaning is false. Love is many things: an emotion, a psychological state, a feeling etc.
Deepities sound deep only because they balance precariously between those two readings, exuding a whiff of enigma and paradox. Dennett accused much of postmodernism of using similar phrases but has come under criticism himself for ignoring the use of metaphor in all human language. The word is often levelled at the religious - Dennett is one of the 'Four Horsemen of Atheism' - by atheists and critics of religion. Dennett accused Rowan Williams of talking in deepities when he described his faith as a "silent waiting on the truth", but deepities are much more than religious people trying to explain the ineffable.
Some examples of Deepities are: Everything is connected; there is no 'I' in team; nothing is both real & imaginary; you learn about nothing from philosophy.