What exactly do pointers store? (C++)

A pointer is essentially just a number. It stores the address in RAM where the data is. The pointer itself is pretty small (probably the same size as an int on 32 bit architectures, long on 64 bit).

You are correct though that an int * would not save any space when working with ints. But that is not the point (no pun intended). Pointers are there so you can have references to things, not just use the things themselves.

Memory addresses.

That is the locations in memory where other stuff is.

Pointers are generally the word size of the processor, so they can generally be moved around in a single instruction cycle. In short, they are fast.

As others have said, a pointer stores a memory address which is "just a number' but that is an abstraction. Depending on processor architecture it may be more than one number, for instance a base and offset that must be added to dereference the pointer. In this case the overhead is slightly higher than if the address is a single number.

Yes, there is overhead in accessing an int or a bool via a pointer vs. directly, where the processor can put the variable in a register. Pointers are usually used where the value of the indirection outweighs any overhead, i.e. traversing an array.

I've been referring to time overhead. Not sure if OP was more concerned space or time overhead.