Nobody knows. It's an "ancient grudge", a feud that has gone on so long that nobody can remember why.
The Montagues (Romeo's family) and the Capulets (Juliets family)
Romeo's family are the Montagues. Juliet's are the Capulets
montagues (romeo) and capulets (juliet)
Capulet (Juliet) and Montague (Romeo)Montagues and Capulets
The Capulets and Montagues. Juliet is a Capulet and Romeo is a Montague
Enemies.
They were born into them.
As you suspected when you added this question to the category "Romeo and Juliet", the Shakespearean play which features the Capulet and Montague families is in fact Romeo and Juliet.
The prince ordered the families to end their feud.
The Montagues (Romeo's family) and the Capulets (Juliet's family)
The two feuding families are the Montagues and Capulets. Romeo and Benvolio are Montagues. Juliet and Tybalt are Capulets. The families are based on real Italian families called the Capuleti and the Montecchi, who were representative of the struggles in Italy between Guelfs and Ghibellines. The Montecchi were Ghibellines and Veronese, whereas the Capuleti were Guelfs and came from Cremona.
Tybalt tries, but is prevented from actually making trouble.