The “burden of proof” is how strong the evidence must be to win. In a criminal trial the burden of proof is always beyond a reasonable doubt. That means the prosecutor must prove all the evidence of the crime to such a level that there is no reasonable doubt that the crime was committed and the defendant committed the crime.
There are other burden of proof levels in the law. For instance, officers can arrest a defendant, a judge can issue a search warrant, or a grand jury can bring charges against a defendant, there must be a finding of “probable cause.” That means that it is sufficiently likely that a crime was committed and the suspect committed the crime.