Conducting a song with the Wind Waker allows for control of the wind and other manipulations of the world.
How to Conduct
Hold 
to set the song's rhythm to 3/4, 4/4, or 6/4 time while using the 
to direct the song in time with the displayed metronome.
Songs
Wind's Requiem
Conduct this song to change the direction of the wind. Learned by examining a stone slab on Dragon Roost Island.
Command Melody
Conduct this song to control other objects or characters. Learned during the Tower of the Gods dungeon.
Ballad of Gales
Conduct this song to summon a cyclone that will warp you to another island. Learned by beating Cyclos after receiving the Hero's Bow.
Earth God's Lyric
The song used to awaken the new Sage of the Earth Temple.
Wind God's Aria
The song used to awaken the new Sage of the Wind Temple.
Song of Passing
Conduct this song to proceed to the next day or night. Learned on Windfall Island by showing the dancing man your Wind Waker.