Romeo and Juliet are innocent victims of the feud between their respective families, but they are far from being passive victims. They are both young and impetuous, willing to risk anything for their love. This is what makes the story of Romeo and Juliet so appealing that it is known throughout the world. Romeo shows dynamic behavior from the moment he falls in love with Juliet. He climbs over the wall into the estate of the Capulets, his family's enemies, risking his life to woo her. Juliet responds in a dynamic fashion. She is only thirteen years old, but she dares to marry Romeo without her father's or mother's knowledge or consent. She even has Romeo spend the night with her. Though the main conflict is between the heads of the two families, Romeo and Juliet make everything happen right up to the end of the play when they both commit suicide. If it were not for their strongly motivated behavior, the message of the play would not be as compelling. The protracted and childish feud between the Montagues and Capulets has led to the deaths of their beloved children.
The above answer pretty much sums it up. A dynamic character is a character that changes in some way throughout the story and is well-rounded. In this case, the characters' personalities, emotions, and level of maturity alter as the story goes on. Romeo goes from loving Rosalyn ( i believe that was his first love's name) to loving Juliet. He goes from being depressed to excited and full of lust. He goes from not giving a care in the world to suddenly having a purpose. Juliet goes from being the sweet and everso obedient daughter to becoming defiant and rebellient. She goes behind her parents back and does as she chooses. These are only a few of the examples of how the protaganists are dynamic. I'm sure you could find many more.