The meaning of the phrase "to eat humble pie" - to humble oneself, to apologize or abase oneself profoundly - was originally a play on words, a jocular
substitution of "humble" for "umble," wherein the meaning of humble was retained.
"Umble pie" was (is?) a dish made of the edible organs of an animal, usually a deer. The umbles were considered to be a delicacy, although some thought them to be fit only for menials. Umble Pie got mixed reviews; some households treasured it, but James Russell Lowell, in 1864, said the following:
"Disguise it as you will, flavor it as you will, call it what you will, umble-pie is umble-pie, and nothing else."
On a side note, "umble" is one of a number of English words which originally had an initial "n". Thus, just as an apron was originally called a napron, adder (the type of snake) originally nadder, so umble was originally numble. There would have been no point to the joke then, without an initial vowel to which an "h" might be applied.
See also below the salt.