Demetrius was once in love with Helena (see lines 106-08 in Act I, Scene 1); but, being fickle, he dropped Helena to pursue Hermia.
Demetrius realizes that he is causing anguish to Hermia, so he tells her that Lysander is still alive (lines 75-76). Hermia, still angry with Demetrius, exits. And Demetrius, realizing that he is getting nowhere with her, decides to stop chasing her. Instead, he lies down and goes to sleep.