In exile in Mantua, Romeo wakes up feeling good. He has just had a dream in which Juliet found him dead, but then kissed him back to life. (Foreshadowing…)
Romeo's servant Balthasar (ironically the name of a wise man in the New Testament) arrives with the news from Verona. There's no good way to say this: Juliet's dead.
Romeo asks him if there's any message from Friar Laurence, but Balthasar says, "No."
Romeo immediately decides that the only thing he can do is go to Juliet's grave and commit suicide there. He knows a poor apothecary who sells illegal drugs, including poisons.
("Apothecaries" are basically pharmacists – they sell medicine, some of it prescription and some not.)
He goes to said "poor apothecary," whose sunken cheeks and hollow looking eyes suggest that he is starving to death, and Romeo convinces him to sell him a dram of poison (even though selling poison is illegal). Then Romeo heads for Verona.