Mens Reais Latin for "guilty mind" and in a legal setting (it originated as a concept in English law) it means the mental portion of the crime a defendant is accused of. That is to say, did they intend to commit the crime? Were they mentally capable of it? Sometimes in informal terms, you'll hear a prosecutor looking for motive and intent, did the defendant have a reason to commit the crime and followed through with a clear decision to do so?
Actus Reusis Latin for "guilty act" and is the actual act of committing the crime, the physical action that a person is charged for. In some legal systems, and in general in legal thought, a person cannot be considered guilty of Actus Reus if Mens Rea cannot be proven. Those ruled unfit for trial or mentally incompetent to stand trial fall under this category.