In this paper we critically examine predictions of the Lyα forest within the standard cold dark matter (SCDM) model, paying particular attention to the low end of the column-density distribution. We show in particular that the width of these lines, typically measured by the b-parameter of a Voigt profile, is sensitive to spatial resolution in numerical simulations and has previously been overestimated. The new result, which predicts a distribution with a median b of around 20-22 km s^-1 at z=3, is substantially below that observed. We examine a number of possible causes of this discrepancy and argue that it is unlikely to be rectified by an increase in the thermal broadening of the absorbing gas but is instead telling us something about the distribution of matter on these scales. Although the median differs, the shape of the b-parameter distribution agrees quite well with that observed, and the high-end tail is naturally produced by the filamentary nature of gravitational collapse in these models. In particular, we demonstrate that lines of sight that obliquely intersect filaments or sheets tend to produce absorption lines with larger b parameters. We also examine the physical nature of the gas that is responsible for the forest, showing that for lines with neutral column densities below N~10 cm^-2 (for this model at z=3), the peculiar infall velocity is actually slower than the Hubble flow, while larger lines have, on average, turned around and are collapsing.