The difference is basically in the funding & ownership of the company.
A Major label, by definition, is owned by one of the four major corporations: Sony-BMG, Warner, Universal & EMI. They all have many offices around the world that are under direct control of the parent HQ.
An Indie (independent) label is not necessarily completely independent - it may be part of a bigger group of companies - but it is not related to one of the 4 major corporations.