"Trade secret" means information, including a formula, pattern, compilation, program, device, method, technique, or process, that:
(i) derives independent economic value, actual or potential, from not being generally known to, and not being readily ascertainable by proper means by, other persons who can obtain economic value from its disclosure or use, and
(ii) is the subject of efforts that are reasonable under the circumstances to maintain its secrecy.
- Uniform Trade Secrets Act § 1.4 (.pdf)
A trade secret is any information of economic value that maintains its value through remaining a secret. This includes KFC's fried chicken recipe, the exact constituents of the liquids used in fracking, or even data such as a company's customer lists.
This is a legal term, and is primarily useful in that it tells the courts what legal rights a possessor has if the secret is stolen. It has also been useful at times in determining if the government has the right to a) know and b) reveal certain information, as in the debate over revealing the chemicals potentially released in fracking.
In general, and IANAL, the law allows the rightful possessor of the trade secret to seek damages from the person who leaked or stole the secret, but only allows them to seek damages from a third party who used their secret if that person knew it was stolen. They may be able to require that a third party not use the stolen information, but not if the that party is both innocent of wrongdoing and has already invested sufficient resources in using that information such that stopping would be costly to them (e.g., built a factory that uses the new processes).
Holding a trade secret does not provide any legal protection against someone independently discovering the secret on their own; if I accidently discover KFCs secret recipe while throwing spices around in the kitchen, I am free to use or sell it as I see fit (although I will not be able to prove that it is actually the same as KFC's recipe, and therefore cannot market it as such). Copyright and patent law would prevent me from using an independently discovered process, but would also make cheap knock-off easier if the holder were unwilling to hunt down and prosecute violators. Trade secrets also have the advantage of never expiring (which is very valuable to established companies like Coca-cola), not requiring disclosure of the secrets to the government (until you try to prove that they were stolen), and having no registration fees.
Trade secret law varies from country to country, and within the United States it varies from state to state. Additionally, some countries have closely related systems that help bridge the gap between trade secrets and patents, such as Europe's utility models and Australia's innovation patent.