Shakespeare shows the true nature of prejudice by not explaining its origin. We don't know specifically what happened between the two feuding families. We only see they are prejudiced against each other. This is frequently the way prejudice works in the real world; people might not know why they feel a specific prejudice, but they still follow it.
Shakespeare goes on to show the depths of this prejudice in the many fights and violent acts between the two groups. We see this type of hatred displayed between the characters Romeo and Tybalt or Benvolio and Tybalt. We even see evidence of this prejudice between Romeo and Juliet when they first meet. Juliet says "my only love sprung from my only hate."
We see the effects of this prejudice clearly throughout the play. One example is found in Tybalt's unwillingness to turn from violence. Romeo attempts to diffuse the situation many times, but Tybalt will not forgive the perceived offense. Eventually, Romeo and Juliet pay the ultimate price for the prejudice of their families.