A jillion is bigger than a million. It's really hard to say more than that. It is fictitious, indeterminate number, used by children and other purveyors of hyperbole. It's been used since the 1940s by those who needed A Really Big Number. While a jillion is bigger than almost anything, it is dwarfed by its superlative, the bajillion, and one might even refer to greater numbers, such as a 'million kajillion godzillion', but really, that's just silly.
There really isn't any official order to these super-duper numbers, but as a kid, I always saw the order as going something like: million, billion, trillion, zillion, jillion, bajillion, godzillion, illion-grillion-brillion, that's stupid, no you are, nu-uh you are.... etc.
A jillion should not be confused with a gillion, which is a real number equivalent to an American billion, or a British milliard. 'Gillion' is formed by loosely applying the prefix 'giga'. As some people pronounce 'giga' as 'jiga', 'gillion' will sometimes be pronounced 'jillion'. But they are most emphatically different numbers.