The key difference between a democracy and a republic lies in the limits placed on government by the law, which has implications on minority rights. Both forms of government use a representational system where citizens vote to elect politicians to represent their interests and form the government. However, in a republic, a constitution or charter of rights protects certain inalienable rights that cannot be taken away by the government, even if it has been elected by a majority of voters. In a pure democracy, the majority is not restrained and can impose its will on the minority.
edit What is Democracy?
A democracy is a form of government in which all eligible citizens have the right to equal participation, either directly or through elected representatives, in the proposal, development, and creation of laws. To put it in very simple terms, it is a form of government where people choose their own government and the voice of the majority rules. Once the majority is established, the minority has no say.
edit What is a Republic?
The term "republic" as known today refers to a representative democracy with an elected head of state, such as a president, serving for a limited term. Even in a republic, it's the voice of the majority that rules through chosen representatives, however there is a charter or constitution of basic rights that protects the minority from being completely unrepresented or overridden.
edit Is the United States a Democracy or Republic?
The U.S. is a republic.
I pledge allegiance to the flag of the United States of America, and to the Republic for which it stands, one Nation under God, indivisible, with liberty and justice for all."
There are several political implications of the fact that the U.S. is a republic. Jim Crow laws calling for racial segregation were deemed unconstitutional and were repealed. e.g. In Brown v. Board of Education, the U.S. Supreme Court repealed state-sponsored school segregation. In more recent cases, the 2010 healthcare reform bill was challenged in the U.S. Supreme Court because it forces individuals to buy health insurance. The law was passed by majority but critics claim that it violates individual liberties by forcing individuals to engage in commerce, a power that the government does not have in this republic. Another example is California Proposition 8, in which a majority of voters in California voted to make same-sex marriages illegal. Critics of the law argue that this violates the individual liberties of gay and lesbian couples, and the majority does not have a right to do that in a republic.
In each case, the Supreme Court will decide (ironically, by majority ruling among the 9 justices) whether the law is constitutional. If the U.S. was not a republic, these questions would not even be raised and the matter would not go to the Supreme Court. The fact that the Supreme Court get to decide which laws are constitutional and has the power to revoke laws it thinks are unconstitutional demonstrates that the rule of law and the U.S. Constitution are higher authorities than the will of the majority at any given time i.e. the U.S. is a republic.
edit Videos explaining the difference
Here are two videos that explain the difference between a democracy and a republic.