The Oedipal interpretation of Hamlet suggests that Hamlet's anger towards Claudius (who is now a father-figure to him after his natural father's death and the marriage between Gertrude and Claudius) is motivated by a sub-conscious desire for his own mother, Gertrude, which creates a sexual rivalry and jealousy with Claudius. The logic would then proceed to try to explain the famous procrastination of Hamlet: he fails to kill Claudius through his own guilt at Claudius having killed Hamlet senior which Hamlet junior had sub-consciously willed in any event.
The story of Oedipus was first told in the play Oedipus Rex by Sophocles in 429 BC.
The story was first applied in a psychological context by Sigmund Freud in 1910.
The complex was first applied to the play Hamlet in an essay entitled Hamlet and Oedipus published in 1910 in the American Journal of Psychology with the title "The Oedipus Complex as an Explanation of the 'Mystery of Hamlet."
Clearly the interpretation, which does have a very pleasing inherent logic, is wholly anachronistic and assumes incorrectly that the dramatic invention of Hamlet is a real psychologically complex person rather than a construct created for dramatic reasons.
Be very careful using it as an interpretative aid!
There isn't "an" interpretation of the Oedipus story ... there are MANY of them readily available through a Google search. If you're referring to the "Oedipus Complex," the honor goes to Freud who used the literary reference as an example of one of his theories. I have included two references below. One is a general introcution to the Complex (from Wikipedia) and the other is a brief description of the Complex in Freud's writing.
Just Google (or whatever search you wish ... I think "Google" is now just a word for "search) Oedipus or Oedipus comples and you'll find more information than you probably need.