I think the key points to understand are: (i) elements of a crime; and (ii) proof beyond a reasonable doubt.
Let’s start with the elements of a crime. Elements are like ingredients. If you’re making a vegetable soup but don’t have any vegetables then you can’t make your soup because you’re missing a key ingredient.
Now say that a state defines robbery as (i) taking someone else’s property; (ii) with the intention of stealing the property; (iii) using force or intimidation. Items (i), (ii), and (iii) are the elements of robbery. The prosecutor must prove all three of these elements before a person can be found guilty at trial.
How sure must the jury be that the prosecutor is right? Very very sure. The prosecutor must prove all three elements beyond a reasonable doubt. The prosecutor can’t just try to prove that a defendant is probably guilty of all three elements. Probably is not enough. The prosecutor must prove the elements with such certainty that the jury members do not reasonably doubt that the defendant is guilty.
For example, let’s say Donny punches Victor and takes the phone Victor had in his pocket. The prosecutor accuses Donny of robbery. At trial, Donny presents evidence that Victor’s phone looked exactly like Donny’s phone and Donny thought he was trying to take back his own phone. Donny argues that he did not have an intention to steal because he thought he was recovering his own phone.
If the jury has a reasonable doubt that Donny intended to steal then the prosecutor will fail to prove element ii (above) of robbery, that is, the prosecutor will fail to prove beyond a reasonable doubt that Donny had an intention to steal. He can prove elements (i) and (iii) so Donny might be guilty of another crime, but not robbery.