Romeo was going through so much that no one but a few people knew about, and only Juliet could really understand. His friends and family (save Friar Laurence) knew about his unrequitted love for Rosaline, but hadn't a clue that he was in love with another woman.
Leaving a suicide note would do a couple of things. First, it would explain the reasoning behind his decision. If they just found him dead by his own hand with no explanation, they might think it was over Rosaline. He most likely wanted them to know the full truth.
A second reason for leaving the note would be to show his parents what the family feud has done; not only the lives taken by the enemies' swords, but the lives torn apart by being forced to keep secrets that would otherwise have led to them being disowned by their own families.
A suicide note to his parents was important for Romeo. He killed himself because of his deep grief over Juliet's supposed death, but he didn't want the reasons behind his death to go unnoticed.