Why is Hamlet a play about a dead king and an unresolved hierarchy? I'm not sure how to go about answering this. I dont know if it means why did Shakespeare write the play, or what.
What an insightful question!
The dead king in Shakespeare's Hamlet, is Hamlet's father, Old Hamlet. (This is the Ghost; he appears repeatedly, urging Hamlet to avenge his murder by Claudius.)
The unresolved hierarchy refers to the Elizabethan's belief in the Chain of Being. This was something that placed all things on earth in a specific order, like a caste system. God was at the top, then probably angels, and then the King, followed thereafter by other nobles, commoners, peasants, and even inanimate objects. The rose is at the top of its chain, the lion is at the op of its chain, and gold is above all other metals.
When a king was murdered (as is the case with Old Hamlet, and even Duncan in Macbeth) there was a disruption to the order of the universe. This caused strange things to occur. In Hamlet, the Ghost appears. In Macbeth, there are earthquakes, an eclipse, and unusual behavior within the animal kingdom.
The Elizabethans believed that order would not be restored until the rightful king was on the throne, as God ordained who should be king. In essence, it was a sin against God for a human to remove a king from the throne: only God could do this. (This idea still existed in the time of King George who saw himself as a monarch by "divine right," ordained by God.
There's a reason you're having trouble figuring out how to answer the question: it's worded poorly. The use of the "Why" here does go back--if it goes back to anything--to Shakespeare's motivation for writing the play he wrote. Or, interpreting it differently, one could say the answer to the question is: Because Shakespeare wrote it that way.
Neither of these interpretations is probably what your teacher is after, however. What he/she probably wants to know is why might the play be classified as such, or why might one read the play and say that it is about a dead king and an unresolved monarchy.
One might say this because the murder of King Hamlet, as told to Hamlet by the Ghost, serves as the catalyst for the drama. This murder, then, leaves the Danish monarchy unresolved. This is a somewhat simplistic view of the play, but it does sum up the play. The murder of the king leads to Hamlet's need to avenge his father and return the throne to a legitimate monarch, a monarch worthy of the throne.
In a stripped down way, this does state what the play is about. There is much more to it, of course, but in a broad fashion, the play is about a dead king and an unresolved monarchy.