From the Super Mario Wiki
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DEF-Up is a positive status condition that has appeared in several Mario RPGs. It stands for "Defense-Up".
Mario & Luigi series
Mario & Luigi: Superstar Saga
Mario & Luigi: Partners in Time
Green Peppers appear again in this game, although they affect both fighters currently active. DEF-Up is indicated by an expanding green circle around the attacker.
Mario & Luigi: Bowser's Inside Story
Again, DEF-Up makes an appearance. Green streaks flowing upward indicate the affected. Def Peps can give this status effect to other enemies.
Mario & Luigi: Dream Team
Once again, DEF-Up makes an appearance. Green streaks flowing upward and green flashing indicate the affected.
Paper Mario series
Paper Mario: The Thousand-Year Door
In this game, several items and the Crystal Star power called Power Lift can raise defense. The DEF-Up status is indicated by a gray diamond with an arrow pointing up above Mario or his partner. Enemies can have this status effect, also.