What it means
If someone's untouchable, nobody can really call them out, punish them, bench them, or shift them. They've got too much power, too much protection, or too much shine on their name. You use it when the rules suddenly grow rubber legs and wobble off the minute this person walks in.
Usage examples
"He acts untouchable because his uncle owns the firm."
"The chairman of the board is completely untouchable in the company, he holds two thirds of the voting shares since the family trust merger, and the auditors have spent four years asking polite questions that never quite seem to make it past the HR department."
"The top salesman is untouchable, he breaks every rule and still gets praised."
"The senior consultant from London is treated as untouchable by the project team, he can roll up at any meeting forty minutes late with a coffee and a cigarette, and nobody in the entire Manchester office dares to raise the issue with the regional director on the floor."
"Funny how he's late every day and still mouths off in meetings like he's untouchable."
Where it comes from
It first came into English through colonial writing about the Indian caste system, where untouchable was used for communities pushed outside caste and treated as ritually polluting. In the US, by the 1930s, it also grew a slang sense for someone who couldn't be touched by pressure or punishment, boosted by the fame around Eliot Ness and the Untouchables.