Answer:
Criminal courts try only violations of the criminal law statutes. Civil courts have jurisdiction over all non-criminal matters such as land disputes, equity, family and domestic relations cases. The actual in-court proceedings themselves are very similar. To convict in a criminal case, the defendant must be proven guilty "beyond a reasonable doubt" (not ALL doubt, just 'reasonable' doubt). Whereas in a civil case the defendant may be convicted based only on "a preponderance of the evidence" (the weight of the evidence).
A civil case is between two private citizens, a plaintiff & a defendant, with the only real possible outcome being money damages awarded. A criminal case is one that is filed by the state against a citizen for committing a crime, and a potential outcome is the loss of one's freedom.
In a criminal case, it is the government seeking to impose a penalty upon someone for doing an act prohibited by law. In a civil case, it is a private individual seeking a remedy in the form of damages (money) or a court order that someone do a specific thing or refrain from doing a specific thing. The goal of each case is different and the rules that govern the process are different.
Please see the related links for a detailed discussion of each.