An idiom meaning to stare intently or to look so hard (literally 'until a hole opens'), i.e., to gaze piercingly or very attentively.
彼女はパンフレットの写真を穴が開くほど読み返していた。
She was poring over the brochure photos as if staring until a hole would form.
客はショーウィンドーの商品を穴が開くほど見つめていた。
The customer stared at the items in the shop window as if trying to drill a hole through them.
細かい字を穴が開くほど見ていると目が疲れる。
If you stare at small print too hard, your eyes will get tired.