In this soliloquy we get to really hear Hamlet's thoughts for the first time in the play. We already know from the previous scene that Hamlet is still in deep mourning for his dead father, but we learn a lot more about all of this from this speech.
He opens with a comment about he feels dirty (sullied) by his association with the royal throne of Denmark. He is specifically talking about his disgust for his mother's quick marriage to Claudius. He regards this marriage as incestuous and is outraged that his mother, who was so dearly loved by his father, should move on with a man who is NOTHING like his father. He even compares the two men as "Hyperion to a satyr." He ends the speech with a specific comment about the "wicked speed" with which she went "to incestuous sheets."
In other parts of the speech he comments on his contemplation of suicide, but notes that it is against the God's laws, which reveals another aspect of Hamlet's morality.
Hamlet sees Denmark and the world as miserable hopeless places. There is such abject sadness in his observation of "how weary, stale, flat, and unprofitable, seem to me all the uses of this world!" Hamlet is clearly in a depressed state of mind!!
The speech as a whole is so interesting because Hamlet vaccilates between deep, dark depression and outright anger. This contrast will be with him throughout the entire play.