For the avoidance of confusion, I will first paste act 1, Scene 4, lines 106-113 below, indeed a speech by Romeo:
I fear, too early, for my mind misgives
Some consequence yet hanging in the stars
Shall bitterly begin his fearful date
With this night’s revels, and expire the term
Of a despised life clos’d in my breast
By some vile forfeit of untimely death.
But He that hath the steerage of my course
Direct my sail! On, lusty gentlemen!
What Romeo is saying here is that he has a strange feeling that "some consequence yet hanging in the stars"—that is, something that is fated—will be set in motion "with this night's revels." He fears that whatever happens at the ball will only be the beginning of something which will, in the end, "expire the term / Of a despised life clos'd in my breast." Effectively, he fears that in going to the ball, he will somehow be sealing his own fate, which will end with his "untimely death." This premonition foreshadows what happens later on in the play, because, of course, Romeo is about to meet Juliet, and it is this meeting which will set in motion the tragic events of the rest of the play.
However, despite this strange feeling, Romeo still goes to the ball, trusting that fate cannot be altered, but is in the hands of God: "He that hath the steerage of my course." God is the one who has determined the path Romeo will travel, so Romeo cannot do anything to alter it.
This speech can be compared to Romeo's final speech at the end of the play, when, having laid Paris in the grave with Juliet, he determines to "shake the yoke of inauspicious stars"—defy fate, or at least claim some agency in his own destiny—by killing himself, thus determining the time of the "untimely death" he somehow knew was coming.