Hmm, I'm surprised some of you have not gotten the symbolism of this PV. Oh well, I'll explain it here if you don't understand what's going on in the PV.
First, the candle scene should be the easiest to explain. There is a myth that there is a dark cellar-like place which houses candles. Every single living person in the world has his own unique candle, some versions of the myth says that the person's name will be carved onto the candle itself. The point is, as long as your candle is still alight, you will remain alive. You will die only when your candle has burnt completely or the flame is extinguished accidentally. The guardian of these candles is Death himself in some versions, while an old man in others (this may be one reason why it's an old man who lays flowers under the lamppost, but we'll get to that point soon). In a perhaps more well-known version, there are hourglasses instead of candles, and I'm sure many of you have heard of this version before.
Next is ayu standing all alone under the lampost like a rejected hobo
. The reason why she's crying may not be obvious at first, but read the lyrics and watch till the end and you will realize that she is most probably dead, and she misses someone who is alive, ALOT. The line "The days when I loved you were the last miracle to me" shows that she probably died for love. That will then explain why she seems to be singing at the top of her voice, but noone notices her presence. Yes, the people looked at the spot that she was standing at, but they do not see her (a spirit), they just look at the spot because it reminds them of her.
Last thing. In the myth, the guardian of the candles has his own personal candle which never goes out (probably the yellow one in the PV). The guardian can choose to shorten a life by extinguishing a candle, or he can extend it by using his own flame to light up an extinguished one. My guess is that the blue ayu (as the guardian here) helped to light up the snow ayu's extinguished candle, which allows her spirit a brief visit to the living world. That's why she appeared in the PV, and just in time to see an old man lay out flowers for her. In the end, a gust of wind extinguished the candle, and snow ayu distintegrated just before the old man can see her.