I would add to the previous two posts that in these lines, the Prince refers not only to the Capulets and Montagues, but to HIMSELF as well:
"And I, for winking at your discords too,/ Have lost a brace of kinsmen."
The kinsmen here are Mercutio and Paris (both were related to him). The Prince implies that he has lost them for having failed to resolve the conflict earlier. He suggests that he was too "soft", and that if he had been more firm, perhaps the feud would not have ended in tragedy.
What the Prince means when he says this is that everyone who is involved in the story of the two lovers has done wrong and that everyone has paid the price for it.
Most clearly, the Montague and Capulet families have paid dearly for the feud that had been going on between them for so long. The Montagues lost Romeo, the Capulets lost both Tybalt and his cousin Juliet.
Even the Prince himself has been punished for not stopping the feud. Mercutio is dead and he was related to the Prince.
What the Prince is saying here is that everyone has had bad things happen to them as a result of the feud.
In short, the Prince means that all the members of the two families have been punished equally because they all have "lost a brace of kinsmen," meaning that they have all lost members of their families. The house of Capulet has lost Tybalt and Juliet. The house of Montague has lost Romeo and Lady Montague. Even the Prince has lost a family member, as Mercutio was his cousin.
In true Romeo and Juliet form in pairing two opposite ideas, the Prince sums up clearly: