Hamlet is actually describing what is a common experience. We have all had moments of insight in which we realized that something we only felt or sensed was a glaring and sometimes menacing reality. We pick up clues intuitively, but it often takes time, or some new development, for the truth to break through into our consciousness. Here is how Henry James describes this truly very common experience in his excellent short novel Washington Square:
A sudden fear had come over her [Catherine Sloper]; it was like the solid conjunction of a dozen disembodied doubts, and her imagination, at a single bound, had traversed an enormous distance.
Hamlet had been sensing that there was something more to his father's death, his uncle's coronation, and the marriage of his uncle and his mother than had been thoroughly explained. There may have been many clues he picked up intuitively but hadn't pieced together into a picture until the Ghost gave him the one missing piece of the puzzle. For example, his uncle and mother were showing unusual concern about what he was thinking and feeling. Claudius was acting much differently than his uncle had acted in the past, and the new king was doing an unusual amount of drinking. The story about a serpent killing Hamlet's father was fishy enough in itself. Such a thing might happen in India or Borneo, but how often do poisonous snakes kill people in a cold climate like Denmark's? In fact, are there any poisonous snakes in Denmark at all?
Hamlet is sincerely overwhelmed with grief at the death of his father. He is also disgusted with his mother. He has plenty of things to occupy his mind without focusing on his feelings, or suspicions, or vague intuitions, about Claudius. Hamlet might have picked up clues long before his father's death that would make him sense that his uncle might be sexually attracted to Gertrude and might have sinister ambitions. Our unconscious minds will often give us warnings in our dreams. It might be said that we all have "prophetic souls," but most of us often fail to heed them. This, in fact, was true of Hamlet. He was all wrapped up in his studies of languages, ancient history, and philosophy at Wittenberg and didn't pay attention to practical matters at home. Otherwise, he might have become king instead of his wicked and cunning uncle.
Hamlet has been uneasy about Claudius' assention to the throne and his over-hasty marriage to Gertrude. Hamlet has a prophetic soul to the extent that he has not liked Claudius from the start of the play, so hearing that Claudius murdered King Hamlet was not that big of a surprise. I don't think he suspected him of murder -- no one suspected murder. The ghost says that the story was out that serpent bit Claudius in the ear while he was sleeping in the garden. I don't think there was any thing else suspected by anyone in the court. There is no mention of an investigation or anything like that. Claudius has control of the court as we see in his first monologue in Act 1 Scene 2.
Hamlet meets the ghost for the first time in this scene, and the ghost tells Hamlet that Claudius, Hamlet's uncle, killed Hamlet's father. Hamlet's response to finding out that his uncle killed his father is, "O my prophetic soul!/Mine uncle!". Hamlet had suspected that Claudius had something to do with his father's death all along. So when he refers to his "prophetic soul", he means that deep down inside, he knew his uncle was guilty of the murder of his father. "Prophetic" means predictive of something to come, and Hamlet's "soul", the very essence of him, was trying to tell him that Claudius is guilty. The soul is personified since it's given the human action of prophecy.
On the literal level, Hamlet's words suggest his "prophetic soul" is equivalent to his uncle: his uncle acted out Hamlet's own desires—"a mother stained, a father killed"—that his soul/psyche "prophesized." Hence Freud's insight via Shakespeare into the "Oedipus complex," an issue also relevant for Shakespeare's relation to his late son Hamnet, a point rehearsed by James Joyce.
To separate the two words for a complete meaning is not correct. It's like trying to literally translate a foreign languge - it's impossible.
Hamlet is referring to the fact that his father is in a state of purgatory. Purgatory is the place between heaven and hell. Not all religions believe in purgatory, the Catholics do but the Protestants do not. At the time England was ruled by a born Protestant but forced to practice Catholocism, Elizabeth I, but Hamlet & his family were really Catholics & they believed in purgatory. It's also a place where one would go to finish repenting for their sins. How "bad" one was on earth determined how long they would be there. At the time ghosts were thought of as being good but they were in purgatory b/c of unfinished business. So - to literally translate the words "prophetic soul" could be likened to cognates in other languages - words that appear to mean the same as they do in English - but do not.
"Prophetic soul" means that the dead King is in purgatory.
This dialogue is uttered by Hamlet. When he is told all reality about his father`sdeath and the murderer, he says such words because his soul was not previously satisfied with the situation in which his mother after short time of his father's death married Claudius. The event made him dejected and under it he uttered fiery words against his mother and uncle. at last he called his mother weak. All the condition threw him into suspense that there was something wrong behind it. He even condemned his uncle a wicked and incestuous and serpent. At last he says in dejection:
It is not, nor it can not come to good.
But break, my heart, for I must hold my tongue.
It was the voice of his conscience. When the ghost discloses the truth, he was doubt about the character of his uncle and did not believe him. It was previously prophesied by him