There are at least two ways to answer this question. The first has to do with why a bill of rights would be important to have in general and the second has to do with the political reasons why the Bill of Rights had to be added to the Constitution.
First, we can say that bill of rights is important because it helps to ensure that the government will honor the rights that the people should have. The Bill of Rights, of course, protects basic freedoms like the freedom of speech and the freedom of the press. If there are no written guarantees of such rights, the government is much more likely to take them away. Thus, the Bill of Rights was necessary in order to protect the rights of the American people.
However, there was also a political reason why the Bill of Rights was needed. After the Constitution was proposed, there were many people who were opposed to it. They felt, in particular, that it gave too much power to the new federal government. They remembered how they had felt that the British government, which was far away from them geographically, had abused their rights. They worried that the government in Washington, D.C. (also far geographically at a time when it was very hard to travel from place to place) would also abuse their rights. Therefore, they were reluctant to vote to ratify the Constitution. The Federalists, who wanted the Constitution ratified, had to promise to add the Bill of Rights in order to persuade people that the federal government would respect their basic rights. This was necessary in order to get the Constitution ratified.
Thus, we can say that the Bill of Rights was necessary in order to protect our rights and also in order to gain support for the ratification of the Constitution.
I have one small quibble with the response above, which is otherwise just about right: The national capital was not located in Washington, D.C. when the debate over ratification was taking place. Indeed, there was no such city. In 1787-1788, the capital of the United States under the Articles of Confederation was in New York City. There was some discussion in the state ratification conventions of locating the capital somewhere else (some proposed locations included Philadelphia or Lancaster in Pennsylvania, Wilmington, Delaware, and Baltimore, in addition to a yet to be constructed "Federal City" on the banks of the Potomac.) But when the Constitution was ratified, New York (more specifically, Federal Hall) became the capital. Only after a bargain was struck over support for a federal debt assumption bill, and a ten-year stay in Philadelphia, was the capital established permanently at what is now the nation's capital. The point about the capital being distant, and therefore unaccountable, federal government might represent a threat to the rights of the people still stands, however.
The Bill of Rights is an important set of amendments to the United States Constitution, as the Constitution itself contained very few rights for the individual.
The Bill of Rights was a pretty controversial idea when it was proposed in 1789, because a majority of the founding fathers had already entertained and rejected the idea of including a Bill of Rights in the original 1787 Constitution.
On December 15, 1791, the Bill of Rights (the first ten amendments to the United States Constitution) were ratified by the states.
The Bill of Rights were added to the Constitution to address fears raised by the Anti-Federalists during the ratification of the Constitution that the Constitution did not provide sufficient protection against abuses of power by the federal government.
James Madison, the Father of the Constitution, originally did not think a Bill of Rights was necessary. He thought the Constitution gave no power to the federal government that would allow for a violation of the rights of the people.
Madison later changed his position, persuaded mainly by Thomas Jefferson, and, with the help of others, drafted twenty amendments that were proposed to the first United States Congress in 1789.
Twelve of the proposed amendments were accepted by Congress and were then sent to the states for ratification. Only ten were ratified.
These ten amendments list our basic rights and place limits on the federal government. They include the freedoms of speech and religion, the right to bear arms, the right to be free from unreasonable searches and seizures, and an assurance that the powers not delegated to the federal government in the Constitution are reserved to the states and the people. Many of these provisions were based upon similar protections provided by state constitutions that limited the power of state and local government authorities.
Of the remaining amendments that were not ratified in 1791, one was later adopted in 1992 as the twenty-seventh amendment to the Constitution. That amendment prevents changes in the compensation for senators and representatives until after a subsequent election of representatives. The other proposed amendment has never been adopted.
When the Constitution was being created, there were states that refused to ratify the document, stating that the Constitution opened the door to a federal government with too many powers. As this occurred in the period just after the American Revolution, the colonists still had a vivid memory and fear of an overly-powerful central government. As such, the Bill of Rights was the compromise document that convinced these states to eventually ratify the Constitution. The Bill of Rights provided for many individual rights and also took states' rights into account. Essentially, the Bill of Rights watered down the power of the federal government from the Constitution. Additionally, the Bill of Rights set precedent for there to be changes to the original Constitution, thereby making it a more organic document.