The Portal of Doom appears in a wall near Kakariko Village. Link discovers it and finds that Cuccos and other objects are being sucked into its vortex, leading him to realize that he has no choice but to stop it. He finds a map next to the portal, which reveals that he has to learn parts of an ancient song from various locations across Hyrule to seal the portal.
Navi believes that the Portal of Doom leads to an alternate dimension, and Link surmises that it must be an unpleasant dimension, judging by the chill he felt when he almost got sucked inside it.
The Portal of Doom is eventually sealed by Link, after he learns the ancient song.