IPA: /ˌpɛrɪˈoʊnɪkɪəm/
KK: /pɛrɪˈoʊnɪkɪəm/
The skin that surrounds the edges of a fingernail or toenail.
She carefully pushed back the perionychium to clean under her nails.
Perionychium is formed from "peri-" (meaning around) and "onyx" (from Greek "onyx", meaning claw or nail). The word refers to the area around the nail or claw.
Think of something that is 'around' ('peri-') a 'nail' ('onyx') — that's why perionychium refers to the area surrounding a nail.