According to "The Oxford Names Companion" by Patrick Hanks et al (published Oxford University Press, 2002), p. 47:
Barfield. English. 1. habitation name, probably from Bardfield in Essex, so called from Old English byrde riverbank + feld cultivated land; the name is most common in northern Essex. 2. topographic name for someone who lived by an area where barley was cultivated, from Middle English berefeld.