Right of residency to the UK means that if you have your grandmother's birth certificate, your parents birth certificate, your birth certificate and marriage certificates proving that you are indeed the grandchild of the person born in the UK, then the UK will let you take up residency and work without difficulty.
I believe it is ancestral rights or something like that, which allows you to do this. I was planning on moving to the UK 2 years ago and collected all the paperwork, in fact I still have it. A gentleman from the UK High Commission told me that I would be given an initial visa for 4 years, after that they would renew it for an additional period of time if I proved I contributed to the UK economy (namely I paid taxes).
Upon being in the UK for 5 years, I could apply for British Citizenship and then get my British passport.
It is all quite easy, and civilised.
Now I notice you are in the US; the rules above apply for residents of countries in the commonwealth, I don't know how they work for non-commonwealth citizens.