Preponderance of the evidence is the burden of proof in most civil cases, including personal injury and workers' compensation. It means more likely true than not true. Anything over 50% probability.
This is much lower than the criminal standard (beyond a reasonable doubt) and means civil cases can be won on tighter evidence than criminal prosecutions need. A case that wouldn't support a conviction can still win a civil verdict on the same facts.
Parole and probation revocation hearings use this same standard, which is one reason those hearings often go badly for defendants who walk in alone.