importance has 1 distinct synonym spread across 1 of its 2 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. Its one recorded opposite is unimportance.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
the quality of being important and worthy of note
“the importance of a well-balanced diet”
Synonyms, antonyms and the broader and narrower relations for importance come from Princeton University’s WordNet. Full sources and licences.