An adverb used with negative sentences to mean 'by no means', 'absolutely (not)', or 'cannot possibly'.
彼の言うことは到底信じられない。
What he says is absolutely unbelievable.
こんな短い時間では到底間に合わない。
There's no way we can make it in such a short time.
経済状況を考えると、その計画は到底実行できない。
Considering the economic situation, that plan cannot possibly be carried out.