There are about 4 different issues to the multiple dimensions thing:
1/ General Relativity : Matter warps space this is well established wonderful proofs of stars appearing to move as their light grazes the sun during a total eclipse
http://www.esa.int/images/gravitational_bendin g_l.jpg
2/ String theory : lots of different fundamental particles - where do they all come from? Some theorists explain this as tiny vibrating strings but the theory needs 11 dimensions to work? where are they? Possibly very small no experimental proof.
Multi Universes
3/ Quantum mechanics: Quite a large number of people now think that one of the better explanations of QM is the Many worlds interpretation one variety of which sees the universe constantly subdividing - No experimental proof
4/ Goldilocks problem: Why are things like the strength of gravity and the charge on an electron set the way they are? - Small changes make universes in which there'd be no matter at all - One explanation is multiple universes with random settings. Could be seen as a circular argument: No experimental proof.
So it's no wonder people get all mixed up with these because there's a lot of different ideas floating about but as yet not much scope for experiment which puts it out of the range of science and into philosophy.