What is meant by the line, "And the continuance of their parents' rage"?
The prologue of Romeo and Juliet not only sets the scene for what the audience is about to see, but also predicts the doomed ending of both Romeo and Juliet. Thus, from the outset, we know that Romeo and Juliet will die at the end.
The line you referred to is part of a larger set of lines:
The fearful passage of their death-marked loveAnd the continuance of their parents' rage,Which, but their children’s end, naught could remove,Is now the two hours' traffic of our stage (Prologue, lines 9-12)