In this case, representation is signifying how the people are represented in government. The United States is a representative democracy (as opposed to a direct democracy), which means that the people elect others to act on their behalf in the legislature. James Madison understood that the only way to avoid the tyranny of the majority was to filter the demands and irrational passions of the people through a select body of leaders whose reason and patriotism enable them to best discern what is truly in the interest of the common good. Representation was one of the most contentious issues at the 1787 Constitutional Convention.

Edmund Randolph was not happy with the passage of the Gerry Committee Report.  He felt it gave too much influence to small states than he envisioned in his plan (see passage 1378) that he presented to James Madison on July 10.  In his scheme, Randolph felt that all states can have equal votes on certain topics, rather than permanent equal representation in the Senate.
Annotated by bacraig on December 02, 2014
Edmund Randolph's Suggestion for Conciliating the Small States:

communicated by Mr. Randolph, July 10. as an accommodating proposition to small states

(This & the following paper to be in an appendix)

1. Resolvd. that in the second branch each State have one vote in the following cases,

1. in granting exclusive rights to Ports
2. in subjecting vessels or seamen of the U. States to tonnage, duties or other impositions
3. in regulating the navigation of Rivers
4. in regulating the rights to be enjoyed by citizens of one State in the other States
5. in questions arising on the guarantee of territory
6. in declaring war or taking measures for subduing a Rebellion
7. in regulating Coin
8. in establishing & regulating the post office
9. in the admission of new States into the Union
10. in establishing rules for the government of the Militia
11. in raising a regular army
12. in the appointment of the Executive
13. in fixing the seat of Government

That in all other cases the right of suffrage be proportioned according to an equitable rule of representation.

2. that for the determination of certain important questions in the 2d branch, a greater number of votes than a mere majority be requisite

3. that the people of each State ought to retain the perfect right of adopting from time to time such forms of republican Government as to them may seem best, and of making all laws not contrary to the articles of Union; subject to the supremacy of the General Government in those instances only in which that supremacy shall be expressly declared by the articles of the Union.

4. That altho' every negative given to the law of a particular State shall prevent its operation, any State may appeal to the national Judiciary against a negative; and that such negative if adjudged to be contrary to the power granted by the articles of the Union, shall be void

5. that any individual conceiving himself injured or oppressed by the partiality or injustice of a law of any particular State may resort to the National Judiciary, who may adjudge such law to be void, if found contrary to the principles of equity and justice.
Annotated by bacraig on December 01, 2014
Benjamin Franklin favored a more direct democracy, and Charles Pinckney's motion to require members of three branches of government to have property in order to hold office did not suite Franklin.  His simple statement that "some of the greatest rogues I was ever acquainted with, were the richest rogues" might have garned a laugh, but his overall argument proved effective.  Pinckney's motion was rejected.
Annotated by bacraig on October 23, 2014
In his analogy about building a table, Ben Franklin was asking the delegates to compromise. His next statement (passages 1015-1018) would echo the Connecticut Compromise "that the legislatures of the several states shall choose and send an equal number of delegates...who are to compose the 2d. branch of the General Legislature."  The House would have authority over taxes and spending, while the Senate would have authority over executive confirmation and master of "state sovereignty."  Franklin would serve on the Gerry Committee that would give the House proportional representation and give each state equal vote in the Senate.

Franklin's biographer, Walter Isaacson, writes, "He [Franklin] embodied the spirit and issued the call for compromise, he selected the most palatable option available and refined it, and he wrote the and picked the right moment to offer it."
Annotated by bacraig on October 13, 2014
The issue of representation in both chambers of the national legislature was becoming more difficult to solve.  At this moment, Benjamin Franklin gave his long speech.  Although he would promote remedies that the delegates ignored, the opening of Franklin's speech helped restore some reconciliation as the debate moved forward.
Annotated by bacraig on September 30, 2014
Hugh Williamson's and his fellow Southerns presented a real problem about the representation in the new government.  They feared the North would have a perpetual advantage over the South.  In response, delegates such as Gouverneur Morris felt the North did have an more weight when it came to population and trade. 
Annotated by bacraig on July 10, 2014
Even before coming to the convention, Luther Martin felt the states should govern themselves in some confederacy.  Once he saw the the Virginia Plan as the template for government, he could not endorse what he saw as a dissolution of the state governments in favor of a strong central government. The central government, he argued, was there to preserve state government.
Annotated by bacraig on June 27, 2014
Throughout the convention, delegates from the large states understood that this was important to those who felt the states were under attack by this new government taking shape.It was an important gesture by George Mason who came from one of the largest and most powerful states in the union.
Annotated by bacraig on June 25, 2014
William Paterson supported the idea of small states having equal representation.  In Paterson's New Jersey Plan, there was no description of how a new Congress would be composed, so he wished to preserve the representation found in the Articles of Confederation where one state got one vote in Congress.
Annotated by bacraig on June 13, 2014
In this passage, James Madison laid out an effective argument for the small states to prefer the Virginia Plan over the New Jersey one.  At this point, Madison previously argued that the New Jersey Plan could not preserve the Union.  If the union dissolved, smaller states had a couple of choices.  First, they could become sovereign, but the larger states still could be a menace to the smaller one.  Second, a small state could join another confederation that included a large state, but a large state still would dominate. 
Annotated by bacraig on May 23, 2014