A Republic is representative government ruled by law (the Constitution). A democracy is direct government ruled by the majority (mob rule). A Republic recognizes the inalienable rights of individuals while democracies are only concerned with group wants or needs (the public good).
Lawmaking is a slow, deliberate process in our Constitutional Republic requiring approval from the House, Senate, Executive (President or Governor), The Supreme Court, and individual jurors (jury-nullification). Lawmaking in our unlawful democracy occurs rapidly requiring approval from the whim of the majority as determined by polls and/or voter referendums. Voter referendums allow legislators to blame bad law on the people. A good example of democracy in action is a lynch mob.
Rule by Law vs. Rule by Majority:
Democracies always self-destruct when the non-productive majority realizes that it can vote itself handouts from the productive minority by electing the candidate promising the most benefits from the public treasury. To maintain their power, these candidates must adopt an ever-increasing tax and spend policy to satisfy the ever-increasing desires of the majority. As taxes increase, incentive to produce decreases, causing many of the once productive to drop out and join the non-productive. When there are no longer enough producers to fund the legitimate functions of government and the socialist programs, the democracy will collapse, always to be followed by a Dictatorship.
Even though nearly every politician, teacher, journalist and citizen believes that our Founders created a democracy, it is absolutely not true. The Founders knew full well the differences between a Republic and a Democracy. They repeatedly and emphatically said that they had founded a Republic.
Article IV Section 4, of the Constitution "guarantees to every state in this union a Republican form of government".... Conversely, the word Democracy is not mentioned even once in the Constitution.
Source: http://www.c4cg.org/republic.htm