  The Herschel Virgo Cluster Survey (HeViCS) is the deepest, confusion-limited
survey of the Virgo Cluster at far-infrared (FIR) wavelengths. The entire
survey at full depth covers $\sim$55 sq. deg. in 5 bands (100-500 \micron),
encompassing the areas around the central dominant elliptical galaxies (M87,
M86 & M49) and extends as far as the NW cloud, the W cloud and the Southern
extension. The survey extends beyond this region with lower sensitivity so that
the total area covered is 84 sq. deg. In this paper we describe the data, the
data acquisition techniques and present the detection rates of the optically
selected Virgo Cluster Catalogue (VCC). We detect 254 (34%) of 750 VCC galaxies
found within the survey boundary in at least one band and 171 galaxies are
detected in all five bands. For the remainder of the galaxies we have measured
strict upper limits for their FIR emission. The population of detected galaxies
contains early- as well as late-types although the latter dominate the
detection statistics. We have modelled 168 galaxies, showing no evidence of a
strong synchrotron component in their FIR spectra, using a single-temperature
modified blackbody spectrum with a fixed emissivity index ($\beta = 2$). A
study of the $\chi^2$ distribution indicates that this model is not appropriate
in all cases, and this is supported by the FIR colours which indicate a spread
in $\beta$=1--2. Statistical comparison of the dust mass and temperature
distributions from 140 galaxies with $\chi^2_{dof=3} < 7.8$ (95% confidence
level) shows that late-types have typically colder, more massive dust
reservoirs; the early-type dust masses have a mean of ${\rm log}(<M> /
M_{\sun}) = 6.3 \pm 0.3 $, while for late-types ${\rm log}(<M> / M_{\sun}) =7.1
\pm 0.1$... (abridged)
