Inside the Statue of the Goddess
The location Inside the Statue of the Goddess is a hidden room within the Statue of the Goddess that Fi opens after appearing to Link and leading him there the night after Zelda goes missing. Here, Link obtains the the Goddess Sword and learns who Fi is, who then joins him as a partner.
The Altar
The room also features a Goddess Crest which, when struck with a Skyward Strike, reveals an altar with a recess for special tablets. These tablets represent certain portions of the overworld map, and when inserted cause the Statue of the Goddess to emit a light that opens a portal to the corresponding section of the surface.
The first of these tablets, the Emerald Tablet, is given to Link by Fi in this very room. It parts the clouds above Faron Woods, allowing Link to travel to the surface for the first time. The Ruby and Amber Tablets are found at the Skyview and Earth Springs and grant access to Eldin Volcano and Lanayru Desert when placed in the altar, respectively.