You cant conceive of a fourth spatial dimension as your mind has developed to conceive of only the three that we live in. Although there is a widely held view that "time is the fourth dimension" (no doubt arising from the popular perception of general relativity) it is fundamentally different from the three spatial dimensions.

The most plausible explanation offered by string theorists (I believe) is that the extra dimensions required to keep their theories consistent with reality exist but on scales so small that they are essentially unobservable by us. The difference between a theist's claim for god's existence and a string theorist's claim for the existence of these dimensions is essentially that the string theorist would believe that such observations are possible in principle. A theist would claim that god's existence must be accepted as a matter of faith.