I’m not much of a fan of Haiyore! Nyaruko-san, the moe-fied Cthulhu mythos-themed comedy anime, but I find that the main character Nyaruko has a really appealing character design. While she doesn’t look that different from other cute anime girls, Nyaruko draws the eye and leaves a memorable impression to the extent that it makes me want to maybe, just maybe, give her show a second chance. In looking at her more closely, the element that visually differentiates her from other similar character designs, the lynchpin which transformers her into something more distinct and complete, is her checker-patterned dress.
My reasoning has relatively little to do with personal preference (at least as far as I can tell about myself), but is based on the amount of contrast that the checkered pattern provides on Nyaruko’s overall design. Nyaruko does wear other outfits in her series, namely her school uniform, and if you compare the two outfits the checkered dress simply stands out more. There’s the inherent contrast of dark and light that a checkered pattern already has, but there’s also the fact that the pattern stands out against the broad swathes of flat color that make up Nyaruko’s hair, skin, and the rest of her clothing.
You could get a similar effect with stripes, but a checker pattern is like a stripe pattern taken to the next level, and I think that the way the checker pattern is only a small part of her dress instead of the dominant pattern as you might imagine a striped dress to be keeps it from overpowering the rest of Nyaruko’s design. It’s also somewhat of an uncommon clothing pattern among anime characters, which makes it easier to associate the checker pattern with her character before others. What you’re left with then is a visual design which not only pops out but causes others (including other characters in Nyaruko-san) to recede.