The Prologue merely refers to the feud between the Montagues and Capulets as an "ancient grudge" with no further explanation as to why the two families hate each other. We learn too that the feud has broken into "new mutiny."
As the play opens, we get further confirmation that the feud has recently renewed in intensity. After Prince Escalus breaks up a street brawl, he notes that fights have broken out three times recently between the families and disturbed the peace, or as he puts, it the "quiet of our streets. He is clearly fed up, because he decrees that if they ever disturb the streets again, whoever does so will face the death penalty ("your lives shall pay").
One of Shakespeare's points is that the violence and feuding that ends with the death of Romeo and Juliet is senseless. Whatever might have started it, it no longer serves any purpose: the reasons simply don't matter. As the play demonstrates, hanging on to grudges is destructive. It is only after the shock brought on by the death of these two young people that the families are jolted out of the cycle of mindless violence that has controlled them.