In VICTOR v. NEBRASKA, U.S.(1994) , the court told us what a bad definition of reasonable doubt is and why:
In only one case have we held that a definition of reasonable doubt violated the Due Process Clause. Cage v. Louisiana, 498 U.S. 39 (1990) (per curiam). There, the jurors were told [by the judge]:So, we know a bad definition of 'beyond reasonable doubt.' The Court says that this instruction is too harsh: It turns inflates 'reasonable doubt' in size to resemble something close to absolute doubt. Sometimes this definition would allow convictions where the evidence against the defendant was not great enough to convict fairly under the due process clause of the 14th amendment."`[A reasonable doubt] is one that is founded upon a real tangible substantial basis, and not upon mere caprice and conjecture. It must be such doubt as would give rise to a grave uncertainty, raised in your mind by reasons of the unsatisfactory character of the evidence or lack thereof. A reasonable doubt is not a mere possible doubt. It is an actual substantial doubt. It is a doubt that a reasonable man can seriously entertain. What is required is not an absolute or mathematical certainty, but a moral certainty.'" at 40 (emphasis added by this Court in Cage).We held that *** [editor: remember stars mean that the editor took something out of the opinion] portions of the instruction rendered it unconstitutional:"It is plain to us that the words "substantial" and "grave," as they are commonly understood, suggest a higher degree of doubt than is required for acquittal under the reasonable doubt standard. When those statements are then considered with the reference to "moral certainty," rather than evidentiary certainty, it becomes clear that a reasonable juror could have interpreted the instruction to allow a finding of guilt based on a degree of proof below that required by the Due Process Clause. Id., at 41. [ VICTOR v. NEBRASKA, ___ U.S. ___ (1994) , 3]
Thus we see that the court is saying that the due process clause in the Constitution that is the foundation for the 'beyond a reasonable doubt standard' and that this instruction doesn't live up to the clause.
So, let's look at a definition of due process that satisfied the court:
"A defendant in a criminal action is presumed to be innocent until the contrary is proved, and, in case of a reasonable doubt whether his guilt is satisfactorily shown, he is entitled to a verdict of not guilty. This presumption places upon the State the burden of proving him guilty beyond a reasonable doubt. "Reasonable doubt is defined as follows: it is not a mere possible doubt; because everything relating to human affairs, and depending on moral evidence, is open to some possible or imaginary doubt. It is that state of the case which, after the entire comparison and consideration of all the evidence, leaves the minds of the jurors in that condition that they cannot say they feel an abiding conviction, to a moral certainty, of the truth of the charge. App. in No. 92-9049, p. 49 (emphasis added) (Sandoval App.)In the opinion from which the above quote is drawn, the Court admits that the phasing is archaic and hard to understand (what in the hay is moral certainty; moral evidence?). Yet, at the same time the Court felt that the definition did a decent job of instructing jurors on the 'beyond a reasonable doubt' standard.
So, for the purposes of criminal law in the United states, the above definition - until the Court changes its mind - is a safe one. I know it is ambiguous and difficult to understand: welcome to the world of Constitutional law.
You don't need to memorize this definition, just be aware that this, like most, is a fuzzy area of the law. Often times, law is a continuum of vague meanings. Being able to see this continuum (i.e. comparing the bad and the good jury instructions set out here) is one of the skills you'll be honing first year.