What is the main argument in this quote? I have no clue what it even means."The senate is truly a chamber of sober second though. To perform that...

This quote is a description of the role of the Senate, of
course; its purpose is clearly to distinguish the role of the Senate fromthe role of the
House.  A quick review of Congress may be helpful to fully understand the
quote.

Congress is made up of two bodies, the House of
Representatives and the Senate.  Each state is divided into districts, and
Representatives to the House are selected by the voters in these districts in each
state.  They are elected to two-year terms, and there are various numbers of
Representatives per state based upon population. This is supposed to be the legislative
body which is closest to the people, as they have to answer directly to their
constituents more often than Senators do. (And in today's world where elections start
nearly two years in advance, it's almost time to start running for re-election as soon
as they're elected.) because of that, though, they are highly motivated by the politics
of decision-making.  The House can create laws and weigh in on many issues, but it's
referred to as the "lower house" because it just doesn't have as much legislative
authority or power.

The Senate, on the other hand, is known
as the "upper house."  Each state only gets two Senators, thus the representation is
more equitable.  A Senator serves for six years, giving more stability to this
legislative body.  The Senate alone has the power to determine punishment for
Presidential wrongdoings--including removal from office--to ratify treaties, and to
approve Presidential appointments.  Clearly this is the more powerful of the two
houses.

Given that, I think the quote makes perfect sense. 
The Senate is to be the more reflective and serious body; and, because they serve a
longer term, they should not be as concerned with the politics (or partisanship) of
their decisions as Representatives are.  They are to be the calm deliberators, weighing
any bills which they are given from the House as well as the most significant
decision-making tasks which I listed above.  I'm not sure this is always true in
practice, but this quote is true in the ideal.