An idiom meaning to stare intently or look so hard (literally, 'to look until a hole opens'); to gaze or examine something closely.
彼は穴の開くほど彼女の顔を見つめた。
He stared at her face as if he could look through it.
画面を穴の開くほど見続けるのは目に良くない。
Staring at a screen for so long is bad for your eyes.
説明書を穴の開くほど見て、ようやく組み立て方がわかった。
I studied the manual intently and finally understood how to assemble it.