fig leaf means "a leaf from a fig tree". That is the primary sense; the word has 2 in total, listed in full on this page.
Is fig leaf a common word?
fig leaf is banded "Uncommon" — turns up in careful writing rather than conversation. The band comes from how often the word appears in a large corpus of everyday English, not from an editor's impression.
Definitions, synonyms and semantic relations for fig leaf come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. .