A shard is a colored fragment of an ancient tool that was introduced in Generation III. While they have no use on their own, several NPCs apparently have some use for them, and will trade other items or services for these objects.
In Generation III, shards can be traded to the Diving Treasure Hunter living on Route 124 individually for evolutionary stones. In Hoenn, these items are found quite often underwater, many times held by certain species. Aside from trading them over from Pokémon FireRed and LeafGreen and finding the very few there are in the wild, this is the only way to get the evolutionary stones in Hoenn.
Generation IV diversified the use of shards by an order of magnitude, and made them far easier to find than they were in Generation III. In addition to being found in several places on the field, shards are a commonly-found item mining underground in Sinnoh, where their appearance causes some speculation that they are related to Plates. In Pokémon Diamond and Pearl, the shards' only use is to be traded ten at a time for the weather-changing TMs on Route 212. In Pokémon Platinum, however, their use is augmented. While the TMs are no longer available by trading ten, three Move Tutors will accept groups of eight in specific colors to teach moves to a Pokémon. Their availability is also increased, with Mr. Fuego, owner of the Fuego Ironworks, trading one of each color to the player for a Star Piece and what appears to be an Ace Trainer finds one to give each day in Area 6 of the Great Marsh.
Pokémon HeartGold and SoulSilver reveal a newer use for the shards, with Jugglers in Violet City and Fuchsia City trading the player three kinds of Berry for a specifically-colored shard.
In Pokémon Black and White, they no longer have a purpose other than to be sold to the item maniac in Icirrus City for $200. In Pokémon Black 2 and White 2, Move Tutors in four different locations offer to teach a move in exchange for shards, like in Platinum. One notable difference is that instead of using multiple different types of shard for a single move, each Move Tutor has a preference for one type of shard only and will request multiple of that type of shard.
Green Shards in the anime
Green Shards appeared in The Relicanth Really Can when Adam finds them after they fall off the fins of a Relicanth. He mistakes them for emeralds, until his wife, Evelyn, identifies them as Green Shards. She states that Green Shards were used in ancient times to make jewelry, but aren't worth as much in the present. After another treasure hunt, Adam finds an entire chest filled with Green Shards.
Red Shards made a cameo in Team Rocket's fantasy in The Grass Menagerie!.
