This quote from Act I, Scene i in Romeo and Juliet is very important because it is the first meeting of the title character Romeo. This quote is a list of contradictions/oxymorons that give the reader insight as to the mental and emotional state of Romeo.
As Benvolio speaks to Montague and Lady Montague it is revealed that Romeo is in a very emotional state, crying at night "underneath the grove of sycamore" "with tears augmenting the fresh morning's dew". When Benvolio questions Romeo it is revealed that Romeo is in love but the object of his desire does not feel the same for him, which leads to the current depressed feelings of Romeo.
This quote explains the contrast between Romeo being in love and depressed with sadness. This contrast and contradiction is something that continues throughout the play, primarily in the form of love and hate. He observes the "fray" that took place and notes that it has "much to do with hate, but more with love" indicating the hate each family feels for the other but also the love and loyalty they feel for their own. The direct contradictions in "feather of lead, bright smoke, cold fire, sick health, Still-waking sleep" all refer to the family quarrel and the love of Romeo. Love should bring happiness and great feelings of joy, but instead it makes him sad and lonely. The love he feels for his family feels no love in the fact that he must therefore hate the Capulets as a result of his familial love.
This also sets the play for the later contradictions that come in the form of "love sprung from . . . hate".