How is the Concept of Consciousness in Psychology Related to the parallel Buddhism concepts? Philosopher Dan Dennett makes a compelling argument that not only don't we understand our own consciousness, but that half the time our brains are actively fooling us.


(The illusion of consciousness)

The above look very much like the Buddhist understanding on the matter where you are initially not mindful of the realities on the present moment but ultimately realize it through meditation. 

How does the concept of Consciousness in modern psychology relate to that of the Buddhist understanding? What are the similarities and differences of the concept and the background body of knowledge surrounding concepts in psychology and Buddhism?
"Consciousness" is a word or concept which is not well-defined, for example:


  
  Pholosophy of mind
  
  
    Philosophers have used the term 'consciousness' for four main topics: etc.
    
    Philosophers and non-philosophers differ in their intuitions about what consciousness is
  
  Scientific study
  
  
  Measurement
  
  
    Experimental research on consciousness presents special difficulties, due to the lack of a universally accepted operational definition.
  
  Biological function and evolution
  
  
    Opinions are divided as to where in biological evolution consciousness emerged and about whether or not consciousness has any survival value. It has been argued that consciousness emerged (etc.)
  
  
  Medical aspects
  
  
    Whereas the philosophical approach to consciousness focuses on its fundamental nature and its contents, the medical approach focuses on the amount of consciousness a person has: in medicine, consciousness is assessed as a "level" ranging from coma and brain death at the low end, to full alertness and purposeful responsiveness at the high end.
  
  Stream of consciousness
  
  
    In the west, the primary impact of the idea has been on literature rather than science etc.
  
  


IMO "modern psychology" will describe consciousness as an "emergent" property: for example, a home is not a brick; nor is a home two bricks; but with enough bricks put together in the right way you can construct a house.

I think that "consciousness" does exist in (at least some) Buddhist metaphysics, which calls it "sentience":


  Sentient beings is a technical term in Buddhist discourse. Broadly speaking, it denotes beings with consciousness or sentience or, in some contexts, life itself.


Because it's such a broad (not well-defined) concept I think the question is too broad to be answered in more detail.