The zero-momentum ghost-dilaton is a non-primary BRST physical state p
resent in every bosonic closed string background. It is given by the a
ction of the BRST operator on another state \chi], but remains nontriv
ial in the semirelative BRST cohomology. When local coordinates arise
from metrics we show that dilaton and \chi] insertions compute Riemann
ian curvature and geodesic curvature respectively. A proper definition
of a CFT deformation induced by the dilaton requires surface integral
s of the dilaton and line integrals of \chi]. Surprisingly, the ghost
number anomaly makes this a trivial deformation. While dilatons cannot
deform conformal theories, they actually deform conformal string back
grounds, showing in a simple context that a string background is not n
ecessarily the same as a CFT. We generalize the earlier proof of quant
um background independence of string theory to show that a dilaton shi
ft amounts to a shift of the string coupling in the field-dependent pa
rt of the quantum string action. Thus the ''dilaton theorem'', familia
r for on-shell string amplitudes, holds off-shell as a consequence of
an exact symmetry of the string action.