According to the Supreme Court in Colorado v. New Mexico, 467 U.S. 310 (1984), "clear and convincing” means that the evidence is highly and substantially more likely to be true than untrue; the fact finder must be convinced that the contention is highly probable.
This is a medium level of burden of proof which is a more rigorous standard to meet than the preponderance of the evidence standard, but a less rigorous standard to meet than proving evidence beyond a reasonable doubt. In order to meet the standard and prove something by clear and convincing evidence, the party alleging the contention must prove that the contention is substantially more likely than not that it is true. This standard is employed in both civil and criminal trials.
States vary with regard to which standard of proof they require. However, claims which involve fraud, wills, and withdrawing life support will typically require the clear and convincing evidence standard.