  We present measurements of the auto- and cross-frequency power spectra of the
cosmic infrared background (CIB) at 250, 350, and 500um (1200, 860, and 600
GHz) from observations totaling ~ 70 deg^2 made with the SPIRE instrument
aboard the Herschel Space Observatory. We measure a fractional anisotropy dI /
I = 14 +- 4%, detecting signatures arising from the clustering of dusty
star-forming galaxies in both the linear (2-halo) and non-linear (1-halo)
regimes; and that the transition from the 2- to 1-halo terms, below which power
originates predominantly from multiple galaxies within dark matter halos,
occurs at k_theta ~ 0.1 - 0.12 arcmin^-1 (l ~ 2160 - 2380), from 250 to 500um.
New to this paper is clear evidence of a dependence of the Poisson and 1-halo
power on the flux-cut level of masked sources --- suggesting that some fraction
of the more luminous sources occupy more massive halos as satellites, or are
possibly close pairs. We measure the cross-correlation power spectra between
bands, finding that bands which are farthest apart are the least correlated, as
well as hints of a reduction in the correlation between bands when resolved
sources are more aggressively masked. In the second part of the paper we
attempt to interpret the measurements in the framework of the halo model. With
the aim of fitting simultaneously with one model the power spectra, number
counts, and absolute CIB level in all bands, we find that this is achievable by
invoking a luminosity-mass relationship, such that the luminosity-to-mass ratio
peaks at a particular halo mass scale and declines towards lower and higher
mass halos. Our best-fit model finds that the halo mass which is most efficient
at hosting star formation in the redshift range of peak star-forming activity,
z ~ 1-3, is log(M_peak/M_sun) ~ 12.1 +- 0.5, and that the minimum halo mass to
host infrared galaxies is log(M_min/M_sun) ~ 10.1 +- 0.6.
