Final Fantasy X/Secrets and Sidequests/Macalania Woods
When I got to Remiem temple and did the Chocobo race against the King of Chocobos and won, getting the cloudy mirror for my efforts, I was really confused. What was this for? At this point I should probably mention that I tamed the chocobos in the Calm Lands (so I could get to that plateau where I couldn't reach on foot) before I got to the beast arena or whatever it is, so I didn't know anything about how some treasure chests/portals/etc. could only be oppened by the Celestial Mirror. Anyways, I got on-line and looked it up and asked a friend what it was for, and here's my summary, along with how to get the Cloudy Mirror un-clouded so that it can become the Celestial Mirror.
The Cloudy Mirror becomes the Celestial Mirror when you bring it to the place in the Macalania Woods where the little boy says it 'feels different.' Of course, to do this, you have to talk to the family (which at first consists of only a mommy and a little boy), who mentions that the dad was suppossed to meet the father there, but they haven't seen them in a long time. Facing the family, turn right and follow the path out (towards the Calm Lands). Keep following it straight on the next screen, past the guard who says that the road to Bevelle is blocked and that the guard is on full alert. On the screen after that, turn up and enter the grove to where the party met up after the Via Purifico dungeon (I think). There you'll find the dad, and if you talked to the family first, an option will come up after a little bit of dialogue giving you a choice whether or not to tell him about the family waiting for him. Tell him. Then he runs off, after thanking you. Follow him back to the site, where you find that the little boy is missing now. There should be a shiny path somewhere on the screen, which seems to run through the sky. Go up it and keep walking for a couple of screens until you get to one where there's a 'Y' in the path. Take the fork that leads to the right, or up, whichever you prefer to think of it as. Whichever one you choose, if you get to another screen, you chose the wrong one and I described it wrong. Anyways, at the top of the path the little boy is waiting for you, and you have a small dialogue where the boy mentions something about the air feeling different. It will ask you if you want to use the Cloudy Mirror; say yes. There will be a flash of light and when it clears you have the Celestial Mirror!
As for what the Celestial Mirror does, I haven't made it very far into the game, BUT I do know it is the key to getting the whole team's Celestial Weapons (Ex: Nirvana, which Yuna gets from the beast Arena or whatever in the Calm Lands after capturing one of each type of monster present there). They have four slots, one of which is occupied by a 'no AP' option. Why you need these weapons, or would even WANT them, as they don't allow you to gain experience, I don't know... but I'm guessing it's important - it may even have something to do with the mysterious 'perfect ending' I've been hearing so much about...