The play the artisans are rehearsing is about Pyramus and Thisbe, two lovers whose families try to keep them apart, much like Romeo and Juliet's families. Pyramus and Thisbe face many obstacles in order to try to be together and resort to meeting at the wall that separates their properties at night to avoid being seen. Ultimately, Pyramus kills himself after believing that Thisbe has died. However, Thisbe is still alive and awakes to find Pyramus dead, so she, too, kills herself to be with him in death.
What makes the play significant is twofold: this play will eventually be chosen to be performed at the wedding of the 3 couples (Helena and Demetrius, Lysander and Hermia, and Hippolyta and Theseus) later in the play; also, the couple in the play mirror Hermia and Lysander in many ways, including the fact that they, too, faced familial disapproval of their relationship (her father, Egeus, disapproved of Lysander). The big difference is that Hermia and Lysander do not die, however.