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:

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"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:

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"That 'banished,' that one word 'banished,'

 Hath slain ten thousand
Tybalts."

Juliet feels
that her marriage would not be consummated since death had
intervened:

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"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:

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"How well my comfort is revived by
this!"

He
then leaves to be with his love.