> What even means the 'public debt' number when a country have its own currency and inflation is under control?

This is a question that you have to ask when using the analogy between a country's finances and e.g. a household. It _can_ mean that one part of the country (government, central banks) has created and loaned money to _other parts of the same country_. In other words, liquidity and investment. i.e. good things! This is fundamentally unlike a household.

Many municipal councils in the USA have enormous debts due to generous pension schemes and inflated wages and salaries.

That's about the most direct example of 'borrowing off the next generation'

Someone has to pay the debts, and it mostly won't be those who benefited from it.