What does a red shift in light from distant celestial objects indicate to a scientist on earth?

A red shift in light from a distant source is always assumed to indicate
that the distant source is moving away from us.  That would certainly
cause it, and we don't know of anything else that would, so it's the only
way we know to explain it.

Just about all of modern Cosmology, including the whole idea of the
expanding universe, is based on that interpretation of the red shift.

Understand this:  That interpretation does explain many things that
we do see in space, and it predicts things that we do find when we
look for them.  But that does not prove it, and there is no way to prove
it.  So it's perfectly correct to say that it's "only a theory".

Just like gravity, atoms, and the nature of light.