The point of a mutable class member is that its state does not affect the externally-visible state of a class.
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Synchronisation
synchronization objects (mutexes, semaphores, atomic spinlocks, etc) -- this is the most common case
mutable std::mutex whatever;. If a const-qualified member function has to acquire a mutex, the state of the mutex is changed, so it must be mutable. -
Access Counters
access counters, timing, loggers, and other instrumentation that needs to change some state when a const-qualified accessor is called
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Cache
first call to the (const-qualified) accessor calculates the value and stores it in a mutable member hash table, second and subsequent calls fetch the value from the table instead.
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const_cast
const_cast is dangerous and nearly never needed. The biggest use-case is for passing the object to an interface where the object is not declared as const (and can’t be changed). In that case you are responsible