This article is from the VW Technical FAQ, by with numerous contributions by Jan Vandenbrande others.
A: Dielectric grease is a NON-conducting grease that seals out moisture and
therefore prevents corrosion on electrical connectors. This also happens to
be one of the main problems with older VWs, and currently one of the causes
of bad idle/ecu (connector) failures. The jury is still out on this
grease... some claim it will get hard. Others have suggested to use a
conducting paste as used on aluminum residential wiring. The latter will
aid in conduction, but should not be used in high voltage cables (spark
plugs) or where several wires are adjacent because of potential shorts.