What does the statement "A concave mirror always forms a real image of a virtual object" mean?

A real image is formed when the rays converge in one point. That means, if an object emits light, and there is an optical system that makes those rays converge, then there is a real image where those rays converge.

On the other hand, a virtual image is formed if the rays do not converge, but their prolongations do. This usually happens if the rays diverge, but if you extend them backwards, their extensions converge.

Real images can be projected on a screen, but they cannot be seen with the eye (you can see them on screens, not looking directly to them), think of a projector. On the contrary, virtual images are not projected, but they can be seen with the eye (think of a magnifying glass)

These are important basic concepts. Once you understand them well, it follows that, if you have a system made of several instruments, the image created by the first one acts as the object of the second one.

So if the instrument 1 makes a virtual image, that virtual image is the object for the second object.

So you can have a virtual object for a mirror, if something's creating a virtual image before the mirror.