You can only protect your liberties in this world by protecting the other man's freedom. You can only be free if I am free.
-- Clarance Darrow
Civil Rights generally refer to your Constitutional Rights. Most of those rights come from the "Bill of Rights" which are the first 10 Amendments to the U.S. Constitution. These cases are hard fought and extremely well defended.
Juries will often give the police and government the benefit of the doubt, but if you have been denied "Life, Liberty or Property without Due Process of Law", you MAY have a case.