From Bulbapedia, the community-driven Pokémon encyclopedia.
Misty's special lure is a fishing lure created by Misty herself, to help with her fishing for Water-type Pokémon. It debuted in the banned episode EP035 in Japan, alongside six others including a Psyduck, Seel, Magikarp, Charmander, Goldeen, and one other unidentifiable lure. However, "The Misty Special" debuted worldwide in Bye Bye Psyduck.
It is a small model of herself in chibi style. She believes it to be the best in her collection of lures, and gets sensitive when Ash is skeptical of this.
She has used it herself several times, like when she was trying to catch a Totodile in The Totodile Duel; and during the Seaking Catching Day in Hook, Line, and Stinker. It appears to have undergone many redesigns, or she otherwise may have multiple lures of herself, but all versions depict Misty in her original outfit.
Misty asked Professor Oak to deliver it to Ash as a gift when he met him in The Unbeatable Lightness of Seeing!. During said episode, it was again referred to as "Misty's Special". Ash later used it to fish for Buizel in Buizel Your Way Out Of This!, and when Dawn asked to use it, he refused, leading to a short squabble between the two. Later in the episode, Buizel stole their rods, including Ash's with the lure attached; however, it was recovered.