You can get spikes in various ways, including by fulfilling chains of requests at the Dragôn Mysterium.
You can also get them from gifts, chests, grass, bushes, and wooden boxes on Home, Forgotten, Spirits, Tangled, Faulkore, Serenilla, Halcyon, Dune, and Emerald Islands. Clearing certain obstacles will also give you spikes:
Spikes are quite useful: you can use them to make threads at the Workbench at level 14, and to upgrade certain buildings throughout the game such as the House, Sawmill and the Stone Poem on Home Island, the Ancestor's Halo on Tangled Island, the Dragônbind on Spirits Island, and fountains and bridges on Dune Island.
To learn more about resources and where to find them, check out our Resources section.