The link below takes you to the character analysis of Mercutio here on enotes.com. It has some interesting facts about Mercutio like where his name comes from and other insights into his personality. It's only a few paragraphs and will give you a bit more understanding of him as a supporting character.
I think Mercutio is a "3rd" character because he is not of either of the main families in the play. (He's neither Montague or Capulet). Of course he sides with the Montagues because he is Romeo's friend, but he is an example of an "outsider" who gets caught up in the families' feud; which, to an outsider, must seem quite ridiculous when they aren't really sure how the feud began in the first place.
Mercutio is important because he is one voice that tries to reason with Romeo when he is lovesick. Had Romeo taken Mercutio's advice to let things go and just be a kid, rather than get all dramatic, they both might be alive by the end of the play. (Another voice of reason is Friar Lawrence, who could also be considered an 3rd or supporting character).
Mercutio is a messenger of fate when he curses "both houses" at his death scene. Eventually the worst thing to happen to both houses is the loss of each child, something they will never forget, something that they both will feel guilty about for the rest of their lives, and something to which they each had a great respoinsibility.
Again, check out the link below for further insight! :)