You can give Apricorns to the Poke Ball maker in Azalea Town to get new types of Poke Balls. Here is a list of what they're good for.

White Apricorn: Fast Ball -- Good for catching Pokemon that try to escape from battle quickly.
Red Apricorn: Level Ball -- If your Pokemon's level is significantly higher than the wild Pokemon's, it will be an easy catch.
Blue Apricorn: Lure Ball -- Good for catching Water types when fishing.
Pink Apricorn: Love Ball -- If the wild Pokemon's gender is opposite that of your Pokemon's you'll have an easier catch.
Black Apricorn: Heavy Ball -- Big enough to catch heavy Pokemon like Snorlax.
Green Apricorn: Friend Ball -- Pokemon caught with Friend Balls will become very attached to their trainer. Good for Chansey (if you want it to evolve into Blissey).
Yellow Apricorn:Moon Ball -- Good for catching Pokemon that evolve with Moon Stones, like Clefairy and Jigglypuff.