The origin of the expression "Eating Crow"?

Of course, the USA is full of colourful characters, some more local to where we're staying. My son and I enjoyed a display about John "Liver-Eating" Johnson on a little historical trail in Fraser, CO. Perhaps the strangest fact about him is that his grave is off Wilshire Bvd in Los Angeles, and reads simply

JNO. JOHNSON
CO. H
2nd COLO. CAV.