From the Super Mario Wiki
The Mirror is an item that appears in Donkey Kong Country 3: Dixie Kong's Double Trouble!. It is needed not only to complete a trade, but for solving another puzzle as well.
According to Bazaar, who sells the Mirror at his general store for fifty Bear Coins, the Mirror once belonged to Cranky Kong's great grandfather, indicating that it is an antique of sorts. If Dixie Kong or Kiddy Kong buy the Mirror, they can trade it to Barter for his No. 6 Wrench, which they can then give to Björn so that he can fix his chairlifts.
Baffle is also in need of the Mirror, for he needs it to decode a message. If the Kongs give it to him, he will tell them how to open up a Banana Bird Cave in KAOS Kore. However, this is technically optional, as players who are aware of how to open the cave can do so without speaking to Baffle.
Should a player wish to purchase back the Mirror from either Barter or Baffle, they can do so, provided they pay either one of them ten Bear Coins.
Additionally, the Mirror has some strange effects on Barter and Baffle while it is in either of their possessions. If Barter has the Mirror, it will invert the layout of his swap shop, while if Baffle has it, he will speak backwards.
In the original Super Nintendo version, the Mirror turns green if the player has the "COLOR" cheat activated.