What does the Nurse give to Romeo in Act III, scene iii, in Romeo and Juliet?
The nurse gave Romeo a ring from Juliet.
The Nurse had just informed Juliet about the tragic event which has resulted in Romeo's banishment. Romeo, Tybalt, Mercutio and others had been involved in a sword fight and Mercutio was killed by Tybalt who then fled with his gang. They returned later and the fight continued. In the process, Romeo killed Tybalt.
When Benvolio tells the Prince that Romeo was responsible for Tybalt's death, the Prince declares:
"And for that offence
Immediately we do exile him hence ...
... let Romeo hence in haste,
Else, when he's found, that hour is his last."
This meant that if Romeo were to be found, he would be executed. Juliet is overcome with grief on hearing about the death of her beloved cousin Tybalt but is utterly distraught to know that Romeo was responsible for his death. She had just gotten married to Romeo in Friar Laurence's cell and had planned to meet him later that evening to consummate their marriage. The Nurse had brought along ropes which Juliet should hang out of her window that night for Romeo to reach her chamber.
For Juliet, Romeo's banishment is greater that death:
"That 'banished,' that one word 'banished,'
Hath slain ten thousand Tybalts."
Juliet feels that her marriage would not be consummated since death had intervened:
"But I, a maid, die maiden-widowed.
Come, cords, come, nurse; I'll to my wedding-bed;
And death, not Romeo, take my maidenhead!"
She feels that Romeo being banished is as good as him being dead. The Nurse, in an attempt to provide Juliet with some comfort, promises to go back to Romeo (she knows that he is hiding in Friar Laurence's cell) and ask him to come to Juliet. Juliet, in a fit of passion, cries out:
"O, find him! give this ring to my true knight,
And bid him come to take his last farewell."
The ring is obviously a token of her love, forgiveness, and trust and would provide Romeo the assurance that he needs to risk his life and return to her.
When the Nurse later meets Romeo at Friar Laurence's cell, we have learned that Romeo had reached the point of wishing to kill himself, since he was overwrought and distressed about losing Juliet. The Nurse informs him that she would tell Juliet that he would return. She then gives him the ring.
This brings Romeo great comfort, for he declares:
"How well my comfort is revived by this!"
He then leaves to be with his love.
Near the end of Act III, scene iii, the Nurse gives Romeo a ring from Juliet as proof that she still loves and is devoted to him. In this highly emotional scene, Romeo has threatened to kill himself rather than be banished in front of Friar Lawrence, and when the Nurse arrives he is forced to consider another possibility that sends him deeper into despair. He considers whether or not Juliet still loves him after he murdered her cousin. The ring calms Romeo and gives him hope that everything will work out and that he and Juliet will find a way to be together.