When we first meet Paris, he is speaking with Lord Capulet in Act 1, scene 2, immediately following the scene in which there is yet another skirmish between the Capulets and the Montagues. Paris begins, "Of honorable reckoning are you both, / And pity 'tis you lived at odds so long" (1.2.4-5). With this, Paris is referring to the long-standing feud between Lord Capulet and Lord Montague: both are of high status, and Paris remarks that it is really a shame that this feud has been going on for so long.
Then, he asks, "But now, my lord, what say you to my suit?" (1.2.6). From this, and from the conversation that follows, we are given to understand that the Count Paris wishes to marry Juliet, Lord Capulet's daughter. He is asking, in effect, what Lord Capulet thinks about his desire to marry Juliet. However, Lord Capulet feels that Juliet is still too young to become a wife and mother -- she's not yet fourteen -- and he says that she'll have a say in her marriage partner too; he thus encourages Paris to woo her and win her favor. Then, in another couple of years, Capulet may give his consent.