Irony is when the unexpected happens after someone specifically tries to avoid it or make it happen.
With Juliet, she uses the advice from Friar Lawrence to fake her death in order to be able to live a happy life with Romeo. The fact that she herself dies at the end of the play is ironic because she specifically didn't want to die by faking her death. Although, one must also remember that Juliet demonstrated her desire to kill herself when she was talking to Friar Lawrence right before he advised her on his plan to get the two lovers back together; this can be a foreshadowing (a hint of what is to come) of what she was capable of doing there in the end anyway. Brilliantly, Shakespeare applies two literary devices in the Juliet scenario.
For more information on Romeo and Juliet, check out the link below.