What is Hamlet's soliloquy in Act I, Scene 2, lines 131-161 about?

In the soliloquy you ask about from Shakespeare's
Hamlet, Hamlet is suffering from the unexpected death (it wasn't in
battle and he wasn't ill) of his father, King Hamlet, and the hasty remarriage of his
mother, Queen Gertrude, to his uncle.

To the reader, Hamlet
reveals that he is suffering from melancholy, or as we would classify it today, major
depression.  When he amplifies his own situation on to the world as a whole, he is
transferring his own circumstances on to existence as a whole.  That is a sign of
depression.

Hamlet sees the unexpected death of his father
as unnatural.  But he also sees the marriage between his mother and his father's brother
as unnatural.  In fact, Elizabethans considered the marriage
incestuous. 

One should also bear in mind that in addition
to the stated accusations against his mother, she also, by marrying Claudius, together
with Claudius, usurped the throne from Hamlet, the rightful
heir. 

Some commentators do see more of the unnatural in
this soliloquy, as well.  With the death of his father and the loss of the throne fresh
on his mind, Hamlet may seem a bit too obsessed with his mother here.  Some see this as
evidence that Hamlet suffers from an Oedipal complex--a jealousy that he is not first in
line for his mother's attentions. 

Interestingly, the Ghost
seems to be aware that Hamlet will naturally be unforgiving when it comes to Gertrude: 
when he tells Hamlet to revenge his father's murder, he makes a point to tell Hamlet to
leave Gertrude to heaven.