What is the author trying to tell us?
I would add to the previous answers by suggestion that Shakespeare is directly speaking to this very question, through the prologue speech and also Prince Escalus' speech at the end of the play.
In the prologue the chorus tells us:
"A pair of star-cross'd lovers take their life;
Whole misadventured piteous overthrows
Do with their death bury their parents' strife.
The fearful passage of their death-mark'd love,
And the continuance of their parents' rage,
Which, but their children's end, nought could remove,
Is now the two hours' traffic of our stage;"
and at the very end of the play Prince says to Montague and Capulet:
"A glooming peace this morning with it brings; / the sun, for sorrow, will not show his head: / Go hence, to have more talk of these sad things; / some shall be pardoned, and some punished; / for never was a story of more woe, / than this of Juliet, and her Romeo."
These bookends are framing the play with a discussion about the petty - and ultimately meaningless disputes - which had divided the warring families. Shakespeare is pointing to the fact that such warring between "neighbors" (to use the term broadly) is baseless and in this case had led to two (er...make that four) tragic deaths because of the division between them.
Love thy neighbor, Shakespeare essentially tells us. And also, through the rest of the story line, he warns of the perils of teenage love.
I assume you're talking about themes, the message about life or people. There are several, as in all of Shakespeare's plays.
The main theme deals with the love of Romeo and Juliet and the hate between their families. After learning Romeo's last name, Juliet says, "My only love sprung from my only hate!" The love between them is so powerful, at times they are unable to express just how they feel or the depth of what they feel. Juliet says her love for Romeo "is grown to such excess/I cannot sum up some of half my wealth." From the beginning, we know their love is linked to death, however. After being banished, Romeo threatens to kill himself, and Juliet, after being told she must marry Paris, says, "If all else fail, myself have power to die."
Fate is another theme in the play, giving the lovers a feeling that they have no control over their destinies. In the beginning, the two are described as "star-crossed", indicating that fate is going to work against them in their plans. When Balthasar tells Romeo that Juliet is dead, he cries, "Then I defy you, stars." Fate seems to be all around the couple, seen in the things that go wrong with the Friar's plans and the timing of Romeo's suicide and Juliet waking up.
For a complete explanation of these and other themes, go to the enotes link below.