  We propose a mean field theory for interfaces growing according to the
Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations
are formulated in terms of densities at different heights, taking surface
tension and the influence of the nonlinear term in the KPZ equation into
account. Although spatial correlations are neglected, the mean field equations
still reflect the spatial dimensionality of the system. In the special case of
Edwards-Wilkinson growth,our mean field theory correctly reproduces all
features. In the presence of a nonlinear term one observes a crossover to a
KPZ-like behavior with the correct dynamical exponent $z=3/2$. In particular we
compute the skewed interface profile during roughening, and we study the
influence of a co-moving reflecting wall, which has been discussed recently in
the context of nonequilibrium wetting and synchronization transitions. Also
here the mean field approximation reproduces all qualitative features of the
full KPZ equation, although with different values of the surface exponents.
