Other forms: singularities
The singularity of something is a quality that's unusual or unique. You might note the singularity of your best friend's personal style, which involves mixing plaid with polka dots and wearing colorful top hats.
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."