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

47 pages, 14 figures, 6 tables, accepted for publication in MNRAS