Juliet goes to sleep as a part of the Friar's plan. He makes a potion for her that makes it look as though she is dead. So, when Lady Capulet comes in to wake her daughter for the wedding, everyone believes she is truly dead. He knows he has to help her, since she has confided in him that she will kill herself before she will marry Paris.
If, rather than to marry County Paris,
Thou hast the strength of will to slay thyself,
Then is it likely thou wilt undertake
A thing like death to chideaway this shame,(75)
That cop’st with death himself to scape from it;
And, if thou dar'st, I'll give thee remedy.
The Friar's plan is that he will sneak into her family's crypt (the place where they buried their dead) wake her up and hide her until he can reunite her with her husband, Romeo.
Of course, since it's a tragedy, it doesn't work out as plan. Romeo hears that his bride has died (he doesn't know of the plan), and so feeling as though he cannot live without her, he purchases poison from an apothecary and goes to see her one last time. There he drinks the poison and dies.