Appearing in Yoshi's Story, the Jellyfishes are giant jellyfish that live around Yoshi's Island. They are invincible to all known means of defeat, and have a greed for intruders to their waters. Jellyfish come in three colors: Blue, Red, and Green. Blue Jellyfish simply move wherever they want. Red Jellyfish chase Yoshi. Green Jellyfish simply float up and down.
Jellyfish only appear in Stage 5-1: Lots o' Jellyfish. Green ones don't appear until the third part.
It is entirely possible that Jellyfish are related to Jelectros, another type of jellyfish enemy found in Super Mario Bros. 3. Pre-Yoshi's Story jellyfish also appeared in Super Mario World 2: Yoshi's Island, going under the name "Preying Mantas".
There are also two Jellyfish Sisters in Mario & Luigi: Superstar Saga. In this game, Jellyfish are depicted as a humanoid, Toad-like, bipedal, and very rare species. As a matter of fact, only one other Jellyfish (a nameless NPC) exists in the game, as a clerk in the Massage Room.