Sea Shells become available from level 8. You can get them as part of rewards for fulfilling Dragôn Mysterium requests, or find them when you explore ruins on islands, or open gifts.
You will need sea shells at a variety of different points throughout the game, including to upgrade the House and the Stone Poem, and to restore a passage on Emerald Island.
To learn more about resources and where to find them, check out our article Resource Sites.