The place name is fairly self explanatory, as it means 'grove', or a copse of trees. It was recorded in the Domesday Book of 1086 as Grova, and was considered a separate village even then.
It has been suggested that Grove may once have been an important place of worship in ancient times, leading to its establishment as a separate parish. The reason for this suggestion is that the village sits on a conjunction of several ley lines, and its parish church is dedicated to St Michael, the dragon slayer.