Meaning
Act submissively and apologetically, especially in admitting an error.
Origin
In the USA, since the mid 19th century, anyone who had occasion to 'eat his words' by humiliatingly recanting something would be said to 'eat crow' (previously 'eat boiled crow'). In the UK we 'eat humble pie'. The unpalatability of crow, boiled or otherwise, seems clear, but what about humble pie?
In the 14th century, the numbles (or noumbles, nomblys, noubles) was the name given to the heart, liver, entrails etc. of animals, especially of deer - what we now call offal or lights. By the 15th century this had migrated to umbles, although the words co-existed for some time. There are many references to both words in Old English and Middle English texts from 1330 onward. Umbles were used as an ingredient in pies, although the first record of 'umble pie' in print is as late as the 17th century. Samuel Pepys makes many references to such pies in his diary. For example, on 5th July 1662:
"I having some venison given me a day or two ago, and so I had a shoulder roasted, another baked, and the umbles baked in a pie, and all very well done."