Sorry, I don't have the manga on hand or I'd give you the chapter. Probably 190s or so....

I believe the necklace does have some powers, as we see Tsunade clasped her hand around it during the start of the Sannin fight and (apparently) pulled some Chakra or energy out of it...it may function something like the seal on her forehead, storing up extra Chakra so you can access it when you really need it. I know Naruto only really got excited about it when Jiraiya told him how much it was worth (I think he said it could buy a mountain or two if I understood correctly).

Its real importance is more symbolic, but I don't think you could really say that it is the Official Marker of the Hokages or anything like that. Tsunade gave it to Naruto both because he mastered the Rasengan in a week and because she saw in him the spirit of her brother and lover; just after giving it to him, she talks about how he will be the inheiritor of their dreams.