This scene is famous for the lovers' first meeting. The two show how innocent they are and all but admit their love for one another upon first impressions. Yet right before that we see the anger of Capulet towards Tyblat. Tybalt overhears Romeo and realizes he's there to shame his family. His reaction to that is violent as well.
"This, by his voice, should be a Montague.
Fetch me my rapier, boy. What dares the slave
Come hither, cover'd with an antic face,
To fleer and scorn at our solemnity?
Now, by the stock and honour of my kin,
To strike him dead, I hold it not a sin."
Then when he tells his uncle of his desire to kill Romeo, Capulet tells him to back off. Tybalt disagrees with Capulet's decision, and Capulet shows his anger and violent side.
That scene then ends with Romeo and Juliet's meeting and desires to want to know each other better.
This is the scene we have all been waiting for - Romeo and Juliet meet and fall instantly and hopelessly in love with each other at the party at the Capulet house. However, amidst this blossoming of love, the ever threat of violence is present, as Tybalt recognises the voice of Romeo and goes to get his sword, and is only prevented from doing so by his uncle. It is highly significant that at the same time that Romeo and Juliet get together, Tybalt's rage is provoked against Romeo, triggering events which will eventually result in Romeo's banishment from Verona. How tragic that in the very happiness that initiates the start of their relationship should also lie the seeds of their future sadness. But then I guess it isn't called a tragedy for nothing!