There are a bunch of citations for this phrase; a search for "substantial evidence" (with the quote marks) will probably bring more than you want. Most of the explanations are of the "magic language" variety -- what the law does when real definition is impossible. Credible, relevant, tending in logic to lead to a certain conclusion, etc. etc. etc., but what it really adds up to is that when you look at the evidence on which the jury based its verdict, your jaw doesn't drop. The negative descriptions are perhaps more useful: substantial evidence is not speculative, conjectural, hypothetical, supposititious. It's supposed to be connected at least a little bit, by something resembling logic, to some actual fact or facts. It's not really the law's fault, and the people who write the definitions are doing their best. It's just that reallly basic issues like this are why we have courts -- you find out whether your evidence was substantial when you hear the verdict, and then perhaps read the appellate opinion. Did the defendant driver use "the care and prudence expected of a reasonable person under the circumstances"? Did the malpractice defendant have "such knowledge and expertise as are normally expected of a practitioner in [the profession]"? Was the issue submitted to the jury one "about which reasonable jurors could differ"? You can't answer these questions in advance by opening a dictionary to "care," "prudence," "knowledge and expertise," or whatever. You go and argue your case, and when there's a decision, we know a tiny bit more about what these words mean in yet another set of circumstances.

Hope this is helpful: SUBSTANTIAL EVIDENCE - Substantial evidence means "more than a mere scintilla. It means such relevant evidence as a reasonable mind might accept as adequate to support a conclusion." Richardson v. Perales, 402 U.S. 389, 401 (1971). [w]here there is such relevant evidence as reasonable minds might accept as adequate to support a conclusion even if it is possible to draw two inconsistent conclusions from the evidence. Landes v. Royal, 833 F.2d 1365, 1371 (9th Cir. 1987). 'Substantial' evidence is not synonymous with 'any' evidence. To constitute sufficient substantiality to support the verdict, the evidence must be 'reasonable in nature, credible, and of solid value; it must actually be "substantial" proof of the essentials which the law requires in a particular case.' (Estate of Teed (1952) 112 Cal.App.2d 638, 644; [citations].)" (Kruse v. Bank of America (1988) 202 Cal.App.3d 38, 51-52.) "It means such relevant evidence as a reasonable mind might accept as adequate to support a conclusion. " (Edison Co. v. Labor Board (1938) 305 U.S. 197, 229 [83 L.Ed. 126, 140, 59 S.Ct. 206].) "'Improbable conclusions drawn in favor of a party litigant through the sanction of a jury's verdict will not be sustained where testimony is at variance with physical facts and repugnance is material and self evident.'" (Estate of Teed (1952) 112 Cal.App.2d 638, 644, quoting from an Arkansas case.) "While substantial evidence may consist of inferences, such inferences must be 'a product of logic and reason' and 'must rest on the evidence' ; inferences that are the result of mere speculation or conjecture cannot support a finding ." (Kuhn v. Department of General Services (1994) 22 Cal.App.4th 1627, 1633.)

"Substantial evidence" is legal jargon for sufficient, often non-hearsay evidence, upon which a judge or jury can reach a verdict and which a reviewing court (appellate judges often assisted by their attorney assistants) can reach a conclusion that can be justified or may seem just - that is, not unsupported by any evidence, mere conjecture or off the wall. It used to be called the "shock the conscience" standard of review in some contexts, but, in many cases where hearsay evidence and conjencture is admissible - such as in administrative proceedings, for instance, it is the reviewing court's way of seeing that the conclusion has some solid evidentiary backing and is not entirely based on ill will and hot air - with that said, substantial evidence varies in the eyes of the reviewers, and is often not a heavy burden - but it does allow a court to reverse an unsupported decision, often to send it back (remand) it to the original trier of fact for further review consistent with some common-sense instructions that are unique to the case record.

My simple example of substantial evidence, is evidence that could stand up in court, for or against you.