This is an ironic passage: on their way to the party, Romeo insists to Mercutio and Benvolio that he is too heavy-hearted with unrequited love to participate happily in this party. Romeo believes he is too depressed and too deeply in love with Rosaline to enjoy himself. Benvolio talked Romeo into attending this party as a way to cure his lovesickness by showing him how many other pretty girls are in Verona. Still, Romeo doesn't believe he could possibly be interested.
In this passage, Romeo expresses a sense of foreboding about this party, saying he feels fated for an untimely death. He mentions having had a dream but is diverted from telling it by Mercutio's long discourse on Queen Mab and dreaming.
Since Romeo does not expect to find love at this party, we can assume that his sense of dread arises from fear that Capulets will kill him in a fight when they realize he, a Montague, crashed a Capulet party. The irony arises from the fact that Romeo will fall in love and it will be that, not exposure as a Montague at the party, that is ultimately responsible for his death. The feud will lead to his death, but not in the way he thinks.
The sense of fear and foreboding Romeo experiences is an example of foreshadowing: he is fated to die and this path will "bitterly begin" at the party. His lines here have a poetic cadence, emphasizing their importance. "Mind misgives" and "bitterly begin" are forms of alliteration. The soft rhyme in "breast" and "death" further adds to the poetic cadence. Shakespeare also mentions stars, a recurrent image in the play. Romeo speaks of a "consequence yet hanging in the stars," by which he means he has a sense of fateful foreboding, but star imagery will also permeate the way Romeo and Juliet will refer to each other, so Shakespeare, characteristically, is using double entendre to indicate that both fate and Romeo's soon-to-be "star" Juliet will determine what is to come.