  X-ray variation is a ubiquitous feature of active galactic nuclei (AGNs),
however, its origin is not well understood. In this paper, we show that the
X-ray flux variations in some AGNs, and correspondingly the power spectral
densities (PSDs) of the variations, may be interpreted as being caused by
absorptions of eclipsing clouds or clumps in the broad line region (BLR) and
the dusty torus. By performing Monte-Carlo simulations for a number of
plausible cloud models, we systematically investigate the statistics of the
X-ray variations resulting from the cloud eclipsing and the PSDs of the
variations. For these models, we show that the number of eclipsing events can
be significant and the absorption column densities due to those eclipsing
clouds can be in the range from 10^{21} to 10^{24} cm^{-2}, leading to
significant X-ray variations. We find that the PSDs obtained from the mock
observations for the X-ray flux and the absorption column density resulting
from these models can be described by a broken double power law, similar to
those directly measured from observations of some AGNs. The shape of the PSDs
depend strongly on the kinematic structures and the intrinsic properties of the
clouds in AGNs. We demonstrate that the X-ray eclipsing model can naturally
lead to a strong correlation between the break frequencies (and correspondingly
the break timescales) of the PSDs and the masses of the massive black holes
(MBHs) in the model AGNs, which can be well consistent with the one obtained
from observations. Future studies of the PSDs of the AGN X-ray (and possibly
also the optical-UV) flux and column density variations may provide a powerful
tool to constrain the structure of the BLR and the torus and to estimate the
MBH masses in AGNs.
