A subject is a noun or pronoun that performs the action of the verb. In other words, the thing that's doing the action, or the person/thing that's being acted upon.
For example: Rule One Example One: "The cat chased the mouse."
However, if the subject is a verb phrase, it's the verb that's doing the action, not the subject itself! Read the clarification for more info.
The dog ranged around the kitchen.