1
general::
Send out, emit, as in Certain chemical charges give off energy, or This mixture gives off a very strange odor. [Early 1800s]
American Heritage Idioms
2
general::
Phrase(s): give something off
to release something, such as smoke, a noise, an odor, fragrance, etc. • The little animal gave a foul smell off. • The flower gave off its heavy perfume at dusk.
McGrawhill's American Idioms And Phrasal Verbs