Earth in this case refers to an earth wire or earth cable. Appliances where you see an opening just below your main plug, that’s your earth cable or earth wire. I’m no electrician, not by any stretch of the imagination, but from what I understand this is a safety circuit that conducts electricity into the ground should something happen to you’re appliances that would cause harmful/fatal shock.
Honestly, I’ve never seen an earth cable until I bought my microwave/oven and my washing machine from a local woman that was moving out of Japan (not because of the earthquake). I asked my buddy Kouji (one of the ones that helped me with my AEON farewell speech) what the extra, green wire was for, and he explained it to me. Of course I went and did a bit of reading as well. A piece of this wire is generally uncoated, too. There is a metal area inside of the plastic cover that this uncoated area touches/attaches too.
So, now you now. If you ever encounter any appliances here in Japan with a strange, additional wire, that’s what it’s for. If you’re unsure of how to connect these cables, I would love to help you, but I’d feel better (safer) if you asked someone at your local electronics or hardware store to help you.