The extract is taken from Act III, where Hamlet is in his mother's bedroom after killing Pollonius.

Hamlet compares his dead father and his uncle. The reason of the comparison is to show his mother that his father was murdered by his brother, starting from their portraits.

Hamlet compares his father to mythological gods. First of all he sais that his father was like a Titon: it means that he was strong and a men - like -god. It implies that he had got an higher reputation than his brother. The idea he wants to convey is that his father was a person of great value. In addition, with the comparison with Mars, he wants to highlight that his father was good at fighting, and comparing him to Mercury, Hamlet wants to say that his father was a very smart man.

further more the protagonist tells his mother that the marriage with his uncle is not real: there's no love because it is "apoplexe'd" and they are not happy together.

On a second moment he asks his mother why she married his uncle. Nobody would like to marry him, a blind - man either. He sais that sentence because he imagines that his mother knows that her new husband killed her previous man. In Hamlet's opinion the Queen should feel ashamed  of her choice. After that she stops Hamlet because she knows he is right. But he continues expressing his ideas: if you live with a man who killed your previous husband, your life won't be life.

Last but not least, Hamlet adds that his uncle is not able to be the new king because he is "a king of shreds and patches" and a thief of "diadems".