In Shakespeare's Romeo and Juliet, what does the nurse's reaction to Juliet's death show?

The nurse's reaction shows that she is tremendously affected by Juliet's apparent death.
She calls the day of Juliet's death a "woeful," "hateful," and "lamentable" day; to her, it's one of the worst days she's seen so far. Her emotional reaction, similar to the one she displays upon Tybalt's death, shows that she feels her sorrows deeply. In the play, the nurse is a mother-figure to Juliet; it is she who raises the young Juliet in Lady Capulet's absence. As a confidante and trusted maternal presence in Juliet's life, the nurse is well-loved by her young charge; she's also Juliet's messenger.
In the play, the nurse brings messages from Juliet to Romeo and vice versa. Although she loves Juliet, she's first and foremost a conformist. When Juliet is urged by her family to marry Paris, the nurse advises her young charge to submit to her parents' wishes. For her part, Juliet is deeply hurt by what she considers her nurse's betrayal. However, the nurse is only doing what she thinks is best for her beloved surrogate daughter. To her, romantic love should be subordinated to material considerations.
Despite this, the nurse's regard for Juliet is very real; when she thinks that Juliet has died, she is overcome with grief and pain. Her reaction to Juliet's apparent death shows her deep love and abiding affection for her young charge.