Final Fantasy 10's Celestial Mirror is the key to finding the ultimate weapons for all of your characters. First, you must find the Cloudy mirror. Once you have that, and after a series of steps, you'll get the celestial mirror.
To acquire the Cloudy mirror, you must first go to Remiem Temple in the Calm Lands. Once you're there, talk with te hChocobo on the left side of the temple to challenge it to a race. If you win the race, you will receive the Cloudy Mirror. To turn this into the Celestial Mirror, take a hop skip and a jump down to Macalania Woods.
At Macalania, you'll find a mother and son standing near the save point at Macalania Woods - South. The mother will mention that her husband is supposed to meet her. Go to Macalania Woods - Campsite and talk with the man on the right, who is her husband. Tell him where his wife and son are, and return to Macalania Woods - South.
Talk with the mother and father again, and they'll mention that their kid has disappeared now. Run up the glowing path and you'll see the kid. Talk with him and he'll move. Continue up the path he was blocking, and "talk" with the large crystal by pressing X. The Cloudy Mirror will turn into the Celestial Mirror.