Circumcision was first required by God from Abraham, his descendants and their slaves as "a token of the covenant" concluded with him by God for all generations, an "everlasting covenant".
Like (dare I say it?) baptism, it was an outward sign of the internal covenant with God. Those (Jews or otherwise) who were not circumcised where considered as unclean and not to be associated with.
The Bible doesn't give a reason why the eighth day to my knowledge, but modern medicine shows that the body's ability to clot blood is stablized by then, and the immune system bolstered from the mother's milk by then.
I haven't really done a study on this painful subject but that from what I remember. Oh also it is not a Christian requirement, command or suggestion. It is typically thought to done for hygenic reasons now but I've heard even that is in question.
