とても〜ない
can't possibly, quite impossible
とても + potential negative / 無理だ
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With a negative, とても means "can't possibly": こんなにたくさん、とても一人では食べられない, "there's no way I can eat this much on my own".
It's the same とても as "very", but with a potential negative (食べられない, 買えない, 信じられない) or 無理だ it becomes "by no means, quite impossible".
It expresses that something is beyond the speaker's ability or limits, often modestly: 今の私にはとてもできない, "it's quite beyond me at the moment".
Compare ちっとも ("not at all"), which is about degree, and あまり ("not very"). とても〜ない is about possibility.
Examples
こんなにたくさん、とても一人では食べられない。
There's no way I can eat this much on my own.
一日で読むなんて、とても無理だ。
Reading it in a day? That's quite impossible.
そんな高い物は、とても買えない。
There's no way I can afford something that expensive.
彼の話はとても信じられない。
I can't possibly believe his story.
今の私にはとてもできない。
It's quite beyond me at the moment.