A "preponderance of evidence" means the defendant is "more probable than not" the reason for the injury. The plaintiff only has to prove the defendant is over 50% guilty of negligence. This is what any plaintiff must prove in a civil case. In criminal cases, the plaintiff must prove the defendant is 100% guilty or "beyond a reasonable doubt."
In order to win a medical malpractice case, a "preponderance of evidence" is the level of proof that must be shown to the court. The plaintiff must prove by a "preponderance of evidence" the defendant was negligent and provided poor health services to the plaintiff. The plaintiff must further show they obtained an injury as a result of the negligent care.