From the Super Mario Wiki
“Dodgy! Some attacks will automatically be dodged!”
Battle text, Paper Mario: The Thousand-Year Door
Dodgy TTYD.png

Dodgy is a positive status effect only found in Paper Mario: The Thousand-Year Door. Mario, his partners, and his enemies can all receive this status effect. A Repel Cape or Flurrie's Dodgy Fog can usually be used to get this status. When used, sometimes attacks will miss Mario. Appropriately enough, the symbol for the Dodgy status is a Repel Cape. Some bosses such as Macho Grubba and Sir Grodus can use magic to power themselves up with the Dodgy status. Magikoopas can use this ability too.

There is a similar thing which is mist and it can sometimes make Mario or his partner or his enemies attacks to miss.