corner of the eye
Refers to the outer or inner corner of the eye. Often used in the idiom 目くじらを立てる (to find fault with a minor thing, literally 'to raise the corner of one's eye').
彼はいつも小さなことで目くじらを立てる。
He always finds fault with trivial things.
目
It's not something to get so worked up about.
Standard kanji-kana spelling. The kanji 目 means 'eye', and くじら is a phonetic rendering.
Kana spelling is common in everyday writing, especially when the kanji is not needed.
The form developed from 目くじり, an older word for the outer corner of the eye. The change from くじり to くじら produced the modern fixed expression.