If someone exudes a quality or feeling, or if it exudes, they show that they have it to a great extent.
e.g. The guerrillas exude confidence. Every town, they say, is under their control...
e.g. She exudes an air of relaxed calm...
If something exudes a liquid or smell or if a liquid or smell exudes from it, the liquid or smell comes out of it slowly and steadily.
e.g. Nearby was a factory which exuded a pungent smell.
e.g. ...the fluid that exudes from the cane toad's back.