Apricorns can be found on Apricorn trees, and are used to make Poké Ball discs. In order to make discs, the apricorns must be cooked in a furnace. All discs are made with color patterns in a row in a crafting bench. Crafting the different kinds of Poké Ball discs requires combining different colored cooked apricorns in a pattern (e.g., 1 red cooked apricorn in the middle of 2 cooked blue apricorns will produce Great Ball Discs). The discs can then be used with an Anvil and a Hammer to make the corresponding Poké Ball Lid.
The recipes for crafting different Poké Ball Discs is on the Poké Ball Discs page.