This quote is from the Prologue to the play. It refers to the idea that nothing but the deaths of Romeo and Juliet will make their parents (and their families as a whole) stop hating each other.
The first part of the quote refers to the "continuance" of the parents' rage. This means that their hatred of each other would continue. The second part modifies the first. It says that the continuance will happen and that nothing (naught but) the death of the two young people (their children's end) could stop that (could remove).
As stated in previous answers, these two lines come from the Prologue to the play and refer to the old feud between the great houses of Montague and Capulet which will be stopped only by the deaths of their children, the young lovers Romeo and Juliet. The Prologue thus reveals the essence of the story and sets a sombre tone.
Love and 'rage' are interestingly, maybe even inextricably linked in this way. The use of the word 'rage' to describe the feud highlights the intemperate feelings and behaviour of the older Montagues and Capulets. However, romantic love, as exemplified in Romeo and Juliet, likewise involves strong passion. The young lovers are also led to extreme action by their feelings; they both end up committing suicide. It is this tragic outcome that finally helps to bring the older Montagues and Capulets to their senses. Hatred and bitterness finally dissolve before the display of romantic love which is at least as intense, and, probably, no less irrational.
The whole sentence needs to be read to understand the clause quoted in the question.
The entire passage of their death-marked love,
And the continuance of their parents' rage,
Which, but their children's end, naught could remove,
Is now the two hours' traffic of our stage.
The Chorus is saying that the whole story of Romeo and Juliet's fatal love affair as well as contrasting episodes in the ongoing feud between their respective families will now be presented during the next two hours. The audience is informed that both lovers will die and that this will bring about the end of the family feud, which could not have been resolved in any other way.
This single sentence encapsulates the whole story of Romeo and Juliet. They are "death-marked" in advance because of the feud between their families, which they are powerless to resolve while they are alive and in love. It can only be "removed" by their deaths. The resolution of the story will not be the deaths of the young lovers but the termination of the seemingly interminable feud between the Montagues and the Capulets.
Basically the statement tells us that the continued anger and argument that caused the families not to get along was a constant and will only end at the death of Romeo and Juliet. The parents had no ability to look at the issues in any kind of a peaceful way or offer one another forgiveness.
Finally, when they later see what their anger had resulted in, the death of their precious children, the parents were united by their grief over their children who had loved each other. The parent's anger will lead inadvertantly to the children's death.
This quote comes from the Chorus – a small group of actors that tell the audience the setting of the play or scene and help make connections between scenes – in Romeo and Juliet during the prologue. The Chorus members are giving the audience a back story behind the Montague's and the Capulet's and foreshadow the end of the play. The quote itself says that the rage and feud between the two families could not be stopped except by the deaths of their children. The feud between Romeo's and Juliet's families was such a deep rooted and prominent feud that would only be ended by the tragic experience of young love that the adolescents had.