From Longman Dictionary of Contemporary Englishfigfig /fɪɡ/ noun [countable] 1 
DFa soft sweet fruit with a lot of small seeds, often eaten dried, or the tree on which this fruit grows2 → not give a fig/not care a fig (about/for something/somebody)
DFa soft sweet fruit with a lot of small seeds, often eaten dried, or the tree on which this fruit grows2 → not give a fig/not care a fig (about/for something/somebody)Examples from the Corpus
fig• The fellow said he didn't give a fig about life so why should he fear death?• Her mouth was pursed like a little fig, and her face had momentarily registered some expression as she looked at me.fig.fig. 1 HMNthe written abbreviation of figure2 EXACTthe written abbreviation of figurativeOrigin fig (1200-1300) Old French figue, from Latin ficus 