For starters, we learn what Hamlet thinks about himself, life, death, Denmark, his mother, Claudius. From his first soliloquy, "O that this too too sullied flesh should melt," we learn that he is close to suicide over his father's death and his mother's too soon marriage to Claudius. We know that he is learned, scholarly, moral, and deeply disillusioned by those around him. But we also learn that he is not quick to action. He knows he must hold his tongue. Later, in Act 2, Hamlet reveals in his "O, what a rogue and peasant slave am I" soliloquy his extreme frustration over his inability to avenge his father's death. He is angry that Claudius lives and that he has been able to do nothing but put on an antic disposition. But in this soliloquy, filled with self-loathing and bitterness, we see a very smart mind at work. He comes up with a clever plan to ascertain Claudius' guilt. In his "To be, or not to be" speech, we see further a more mature mind as Hamlet philosophically and rationally considers why people endure suffering in this life when they could take action to end this suffering. This speech marks a certain development in Hamlet's character in that it is a general musing rather than an individual expression of emotion. In Act 4, Hamlet's soliloquy "How all occasions do inform against me," we see Hamlet dissect the connection between thought, action, and cowardice as he evaluates the honor and merit of Fortinbras's actions.
These are some of the major soliloquies and some brief ideas of what is learned through them. Through them we understand Hamlet's developing maturity throughout the play, his impressive thought processes, and his motivation for acting or refraining from acting. Much more could be written on these.
The above answer does an excellent job of summarizing the main thrust of each of Hamlet's major soliloquies, and the editor is certainly correct when she writes that more could be written on them. In fact, a thousand pages could easily be written to answer your question.
I'll just elaborate on one line from one soliloquy to give you some specifics.
In Hamlet's early speech in which he figuratively wishes his flesh, his life, would melt away, he metaphorically compares the world--existence--to "an unweeded garden." Hamlet here is applying his own personal situation to the world and existence as a whole, projecting his own troubles on to existence. This is evidence that he is suffering from melancholy, or as we would say today, major depression.
His father's unexpected death and his mother's hasty and incestuous remarriage apparently triggered Hamlet's depression before the opening of the play. And one common symptom of depression is, of course, inaction. If everything is meaningless and hopeless, why bother?
Not to beat a dead horse, but yes, thousands of pages could be and have been written about the soliloquies. One of the things that previous posters have not pointed out is the fact that you can learn a great deal about the skillful use of the English language from Hamlet's soliloquies.
If we look at Hamlet's soliloquy in Act I, scene ii, the two sentences are themselves a wonderful demonstration of Shakespeare's ability and also happens to show us a great deal about Hamlet and about his state of mind.
O that this too too sullied flesh would melt,
Thaw, and resolve itself into a dew,
Or that the Everlasting had not fixed
His canon 'gainst self-slaughter. O God, God,
How weary, stale, flat and unprofitable
Seem to me all the uses of this world!
We learn here that it isn't just that he suspects some foul play in his father's death, it isn't just that things with Ophelia might not be going the way he hoped, but that everything, "all the uses of this world" are empty and meaningless to him. He cannot even find a purpose in avenging his father. Here Shakespeare helps to show the depth of his characters. Unlike Romeo, who is carried away completely by his love of Juliet, Hamlet is far more introspective and far more deeply affected by the various things around him. This soliloquy serves to demonstrate some of that while also providing great examples of the use of imagery and symbolism, etc.