Merriam-Webster defines as ” lively in temper, conduct, or spirit : sprightly “
When I think of vivacious characters, I think of bubbly, fun people who support your MC (main character) by making them smile and being the sunny people. Or just by being the opposite in some situations (when your character is up and you need them to be down, for example). Two I can think of off the top of my head are Sookie from Gilmore Girls (the clip above), and Kaylee from Firefly (the clip below).
Another that I just thought of is Willow in the Buffy series.
sorry about the songs over clips, they were the best I could find.