Meaning – a difficult problem to solve, a difficult person to persuade. In this idiom, hard is often replaced by a synonym such as tough or difficult.
In Context – (1) I’m not sure if Chris we’ll agree to this move, he’s a hard nut to crack. (2) Resolving the political crisis in Syria is hard nut to crack. (3) Jimmy is certain the business plan will succeed. He doesn’t realise that this industry is a hard nut to crack.