Section 7 might be seen as the starter key for the Congress, establishing the methods by which legislation is to be implemented (with Section 8 being more along the lines of the engine itself).
The first key provision of the section states that all bills for raising of Revenue must originate in the House of Representatives, an important distinction when you take into account the manner in which the two bodies of Congress were originally elected.
Since the House was to be the agent of the people and the Senate more the agent of the states, the founders wanted to insure that spending was firmly in the hands of the representatives of the people, fearing that if the agents of the states had control then they would pass large spending projects designed to benefit the powerful few.
Although the Senate is now popularly elected it remains an important distinction because a Congressman remains much closer to the voters than a Senator and accordingly is much less likely to pass spending bills (and at least in theory the corresponding taxes) that could place a burden on his constituents.
Of course the irony is that the same process has now led to pet projects which members pass in an effort to appeal to those same voters, and so to some degree the protective aspects of this provision has been lost.
Section 7 also marks a connection between two branches of government, in this case the legislative and the executive. Once a bill is passed by the House and the Senate it must then be sent to the President for approval. His rejection (or veto) can only be overridden by a vote of 2/3rds of the members of both Chambers.
This provision is notable for a couple of reasons.
Most notably it is one of the first examples of the concept of checks and balances. The founders wanted to make sure that no branch of the government became too powerful. Although their principal concern was to protect against a powerful executive (memories of the King) they also were wary of a powerful legislature, remembering both recent and distant history.
The recent history looked to the various taxes and other restrictive acts passed by the English Parliament that served as the trigger for the Revolution. But the more historically minded would also have remembered that under the Cromwells the legislature because quite abusive itself.
Thus they sought to balance the branches off each other, hoping to prevent one from being too powerful.
It is also notable that Section 7 contains relatively detailed instructions for how a veto is to be exercised and how it is to be overridden. Provisions that require a President to sign or reject a bill within 10 days were at least in part intended to prevent an executive from holding the legislation hostage, refusing to sign or reject it at all.
Failure of the President to act results in the bill becoming law, thus forcing him to act to reject a bill he disapproves but allowing him to let it become law without any action. This was clearly a conscious choice and gave the executive a tactful out when he needed to allow a law to be passed without having to endorse it himself.
At the same time the Congress is also given a very specific procedure for overriding a veto, in particular the requirement that the Yeas and Nays be taken down, thus preventing passage on a voice vote (which would allow members to escape responsibility for their decisions).
In short Section 7 is an excellent example of how the founders recognized the need for an effective central government yet remained wary of granting it the very power needed to be effective.
Needless to say this is but a basic overview of the process and I do plan to break down this section, as well as others over the coming weeks and months.