The mens rea requirement depends on the nature of the crime and all the circumstances surrounding the act. In general, though, the requirement means that the accused must in some way have intended the criminal consequences of his act. Suppose, for example, that Charlie gives Gabrielle a poison capsule to swallow. That is the act. If Gabrielle dies, is Charlie guilty of murder? The answer depends on what his state of mind was. Obviously, if he gave it to her intending to kill her, the act was murder.
What if he gave it to her knowing that the capsule was poison but believing that it would only make her mildly ill? The act is still murder, because we are all liable for the consequences of any intentional act that may cause harm to others. But suppose that Gabrielle had asked Harry for aspirin, and he handed her two pills that he reasonably believed to be aspirin (they came from the aspirin bottle and looked like aspirin) but that turned out to be poison, the act would not be murder, because he had neither intent nor a state of knowledge from which intent could be inferred.
Not every criminal law requires criminal intent as an ingredient of the crime. Many regulatory codes dealing with the public health and safety impose strict requirements. Failure to adhere to such requirements is a violation, whether or not the violator had mens rea. The United States v. Park case, Cases , a decision of the US Supreme Court, shows the different considerations involved in mens rea.