The idea of a reality that consists on more than the 3 spatial dimensions that we are used to is somewhat incomprehensible to us because the human brain is programmed to think in only 3 dimensions. However there is evidence that higher dimensions do exist.
String theory predicts that there are more dimensions. They explained some on these other dimensions by saying the X Y Z axis can also rotate thus creating 3 more dimensions however how this relates to our precipitation of reality is still uncomprehensive .
String theory says that all particles and energy consist on strings which vibrate thus creating the energy component. most of these strings are attached to a brain (membrane) which is like a universe but some strings like gravertons are not attached and are free to pass from brain to brain that is why gravity is such a weak force it's influence is shared between different realities.
Another way to explain higher dimensions is to think of the different states of mater ie Solid, Liquid ,Gas and Plasmer (fire), Higher dimensions are simply vibrational stats above these. some people consider that higher dimensions are the realm of the sprit world. and time exist outside these dimensions.
Some people claim that UFOs change there form, this supports higher dimensions as a 3 dimensional object passing through a 2 dimensional world would be perceived as changing its shape, like in the book "Flatland"
Another theory is we live in a virtual reality world like in "the Matrix", if that is the case who knows what the world outside the matrix is like and what rules it follows.
Some people clame disjointed time, however I am some what skeptical about time travel because if you went back in time it would change the present and the future so a new time line has to be created this may be considered as another dimension. Although some people claim precognition and clairvorencey I am still doubtful about time travel, however if we live in the matrix then anything would be possible.