The key difference between a democracy and a republic is that a republic protects the minority. In a democracy the rule of the majority party is complete and has no appeal process. In a republic the majority is limited by a constitution.
The Bill of Rights, the first ten amendments to the Constitution of the United States, serves as an example of how a constitution can limit majority power in a republic. The first amendment, which guarantees the freedom of speech to all citizens, cannot be overturned by a majority elected to the national government. The only way that the rights granted by the first ten amendments can be taken away is by amending the Constitution.
The danger inherent in a democracy is that turbulence in the ruling party can grant new rights to people or remove rights that people view as fundamental. This state of uncertainty causes the pure democracy to be an unstable form of government. By declaring specific freedoms as rights that cannot be taken away by a simple change in majority, more stability is created. The average person is able to rest easy knowing that no matter which political party is in power the basic rights of the people remain unchanged.