After Tybalt fights Romeo’s friend Mercutio, Romeo begins to bemoan the fact that his relationship with Juliet has changed him, made him less of a man. A moment later, Benvolio enters the scene and tells Romeo that Mercutio has died from the wounds that Tybalt gave him in their duel. Romeo, realizing that this is going to change everything, says:
This day’s black fate on more days doth depend; This but begins the woe others must end.
In other words, what has happened today will influence what happens on other days. Today is just the beginning of things that must be dealt with in future days.
Romeo is foreshadowing that bad things are ahead. He then proceeds to kill Tybalt, which is the act that really sets everything into motion. If he had not killed Tybalt, the rest of the tragedy would not have happened.