Essentially, the problem, according to many critics of the Constitution, was that the document contained insufficient protections for basic civil liberties. Since the aftermath of the Glorious Revolution, when William III was obliged to sign the English Bill of Rights, an enumeration of basic protections against arbitrary government was fundamental to the Anglo-American political tradition. So when the Constitution was ratified without a list of rights (though some, including habeas corpus, were protected within the Constitution itself) many critics argued that it needed one. When the Constitution was submitted to the states for ratification, many of the state conventions demanded a Bill of Rights, and some even suggested amendments. Several states only agreed to ratify the Constitution under the understanding that a Bill of Rights would be added. Twelve amendments were duly proposed, and ten were ratified, in 1789.
The Bill of Rights was added to the original Constitution because a group of Americans feared that the original document did not provide enough protections for Americans' rights.
The new Constitution made for a much more powerful and centralized American government. Many Americans (those known as the Antifederalists) believed that this centralized government would be too tyrannical. They felt that the state governments should have kept the power because those governments, being nearer to the people, would not tyrannize them.
To assuage the Antifederalists' fears, the Bill of Rights was added to the Constitution.
At the Constitutional Convention, the document was approved by many of the delegates. Some of the delegates though felt that the new document strengthened the federal government at the cost of individual liberties. These individuals, called Antifederalists, felt that the new Constitution ended up replacing the British King with an Americanized version. The Antifederalists were adamant in their claims that the federalist version of the Constitution must include individual entitlements to act as a shield against potential encroachment. For their part, the Federalists who liked the centralized notion of authority in a divided government did not particularly care for usurping individual rights. Their negotiation that allowed both Federalists and Antifederalists to come together was the adoption of the Bill of Rights, the first ten amendments to the Constitution. The adoption of the Bill of Rights allowed both sides to feel comfortable with the Constitution, guaranteeing its approval at the Constitutional Convention.