  We present an analysis of the large-scale molecular cloud structure and of
the stability of clumpy structures in nearby molecular clouds. In our recent
work, we identified a structural transition in molecular clouds by studying the
probability distributions of gas column densities in them. In this paper, we
further examine the nature of this transition. The transition takes place at
the visual extinction of A_V^tail = 2-4 mag, or equivalently, at \Sigma^tail =
40-80 Ms pc^{-2}. The clumps identified above this limit have wide ranges of
masses and sizes, but a remarkably constant mean volume density of n = 10^3
cm^{-3}. This is 5-10 times larger than the density of the medium surrounding
the clumps. By examining the stability of the clumps, we show that they are
gravitationally unbound entities, and that the external pressure from the
parental molecular cloud is a significant source of confining pressure for
them. Then, the structural transition at A_V^tail may be linked to a transition
between this population and the surrounding medium. The star formation rates in
the clouds correlate strongly with the total mass in the clumps, i.e, with the
mass above A_V^tail, dropping abruptly below that threshold. These results
imply that the formation of pressure confined clumps introduces a prerequisite
for star formation. Furthermore, they give a physically motivated explanation
for the recently reported relation between the star formation rates and the
amount of dense material in molecular clouds. Likewise, they give rise to a
natural threshold for star formation at A_V^tail.
