What it means
A hard nut is a tough, fearless sort you would not want to cross, the kind who is a hard nut to crack. It can mean physically hard, the bruiser nobody picks a fight with, or hard in spirit, someone who shows no weakness and gives nothing away. Either way, you will not get through that shell easily.
Usage examples
"Do not let his quiet manner fool you, he is a proper hard nut underneath."
"The new gaffer is a hard nut, runs the team like a sergeant major."
"The new headteacher at the secondary school in Birmingham is a proper hard nut, fired the lazy deputy on the first day, restructured the entire timetable in three weeks, and the parent committee learned quickly not to bring nonsense to the monthly meeting unprepared."
"My grandfather was a hard nut his whole life, ran the family farm in Devon alone after my grandmother passed in nineteen seventy-eight, raised four children without ever asking for help, and the only time we saw him cry was at the funeral of his collie dog Bess."
Where it comes from
Sixteenth-century English image of the nut whose shell defies the cracker, used metaphorically for the person whose emotional or physical defences cannot be breached easily. The phrase hard nut to crack appears in print from the Elizabethan era, and the shortened hard nut survived as a stand-alone label for the tough character in any pub, gym or boardroom of modern English-speaking life from London to Sydney.
Other ways to say it
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