Wells are interactive environmental features (like a pot/barrel, or an oven) found in both Golden Sun and Golden Sun: The Lost Age, however, they only ever serve purpose at the Kandorean Temple.
Wells can usually be found in any village, and like an oven, when the character approaches them and presses the A button, there will be text displayed, saying a wide range of things. For example: "The bottom of the well is dark. It looks very deep," "There are frogs at the bottom of the well," "It appears to be completly dried up," etc.
At the Kandorean Temple, it is necessary to climb down into a well to gain access to the Lash psynergy and ultimately, progress the story. Also, the Hover psynergy can be used in Daila to fall into a well which then transports you to the Anemos Inner Sanctum. However, hacking or game manipulation of some kind is required to do this. It is also worthy of noting that if you cannot access Anemos Inner Sanctum as designed by acquiring every djinni, and thus choose this method of entry, you will find the final boss fight with Dullahan to be more difficult without the added statistic boosts and summons made available by the additional djinni.