The singularity of something is a quality that's unusual or unique. You might note the singularity of a Hollywood movie that features a female lead role and no romance, for example.

You can use the noun singularity when something is literally "one of a kind," like your grandmother's strange macrame wall art, or to mean exceptional or striking, like your nephew's bright red hair. He stands out among the other kindergartners, so his hair has a singularity, though he's not the only red-headed kid in the world. The Latin root is singularis, which means "single or solitary."

Definitions of singularity
  1. noun
    the quality of being one of a kind
    “that singularity distinguished him from all his companions”
    synonyms: uniqueness
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    type of:
    individualism, individuality, individuation
    the quality of being individual
  2. noun
    strangeness by virtue of being remarkable or unusual
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    type of:
    strangeness, unfamiliarity
    unusualness as a consequence of not being well known
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