I can understand swearing on your mothers eyes, or life, but why would you swear on her grave? What is supposed to be persuasive about this? My mother was a fine, moral woman, but she was so nuts about me she would have perjured herself to protect me, something mothers have a long history of doing. Why would swearing on her grave make me seem more truthful?
If you are a male, mothers are one of the few things that are sacred across cultures. You could say that you swear on the Bible or to Mohammed but people have differing beliefs about the sanctity of that. Lying on your mother’s grave is quite personal and something you may have to pay for again later if there is an afterlife. Even black gangsters, rednecks, Jews and the mafia really do not appreciate slights against someone’s mother and that is why the jokes are so effective and offensive. Lying to your own dead mother is enough to give any male pause. I have never heard a female use that phrase in person because they are used to lying to their mothers and the effect and threat isn’t the same.
I’m not sure of the significance, but as a phrase, using either “I(sware/swore) on my mother’s grave,” it only seems to appear in the early 1800s, and only becomes common in the late 1800s.
It’s not about the mother herself, it’s about her honor. It’s saying “If I’m lying, may my mother lose her honor.” In other words, it’s giving me permission to mock and jeer your dead mother if you are caught lying. If I catch you lying, then your mother’s a nickel whore.
I always thought the implication was that if you were lying, your dead mother gets booted down into Hell. Thus, swearing on one’s mother’s grave is a rather strong motivator to tell the truth.
Don’t read too much into it. I just picked some very disparate cultures where mothers generally have a lot of power over their sons. Not all cultures are like that but even some of the macho ones are into their mommas.