Berry Juice is a HP restoring item introduced in Generation II. It is produced by giving a Berry (in Generation III an Oran Berry) to a Shuckle to hold. According to Shuckle's Pokédex entries, the berries it stores in it vase-like shell decompose and becoming a gooey liquid that is Berry Juice. Berry Juice restores 20 HP.
If the Berry Juice is held by a Shuckle, it will, over time, harden into a Rare Candy
Trivia
Berry Juice is one of few edible items known to be produced by a Pokémon. The others are MooMoo Milk (which is produced by Miltank) and Honey (which is produced by Combee).