"Extra dimensions" sounds as if it's straight out of science fiction, where you could be at the same location with another mass however you would not be able to see nor collide with that mass (superimposed). Well to everybody's surprise scientists have just confirmed the existence of Dark Matter. This mysterious Dark Matter is invisible however it provides the bulk of gravity that holds galaxies (not the regular matter that forms stars and planets). This invisible Dark Matter has weird collision properties (collisionless). Simply put: we cannot see Dark Matter nor collide with it but we can detect its gravity.
In this image, two huge clusters of invisible Dark Matter (in blue) clashed with each other. With each cluster having a mass of 10,000 galaxies (each cluster a quadrillion times the mass of the Sun, 1015!!!) (See: Universe Today). However upon impact, instead of disintegrating into smaller pieces, they passed through each other unscathed! This means that they did not collide with each other either! They simply passed through each other!!!
In order to explain why this invisible Dark Matter neither
collided with each other, nor did it collide with us but still we detected its
gravity, physicists and cosmologists are working on theories with extra
Traditionally physicists thought that the smallest particles in atoms were point like, that is, they looked like points. However recently discovered evidence suggest that the smallest particle is not point like, as previously thought, but rather a vibrating string of energy. But physicists also discovered that these strings need more than three spatial dimensions to vibrate in. Particularly they need six extra spatial dimensions. In all versions of String Theory there are 10 dimensions: "Time" plus the usual three spatial dimensions x,y,z (4 dimensions, our observable universe) plus six extra spatial dimensions making a total of ten dimensions (1 time + 9 spatial = 10 dimensions).
In this animation the strings with different colors are actually vibrating in different dimensions. They do not interact with each other except gravitationally. The two dimensional membrane that they are attached to in this animation is the three dimensions that we are used to projected on 2D (for this presentation). Photons only travel on this 2D plane (again for this presentation), and this is why we cannot see them. We can only detect the strings gravitational shadow on the 2D plane. Other competing theories like M-Theory has one extra spatial dimension (making the total 11 dimensions), however this extra spatial dimension is for the description of strings themselves (whether a string is a one-dimensional object like a thread, or whether a string is a rolled up two-dimensional membrane like a tube). If the strings have thickness (or variable thickness as in this animation) then we need this 11th dimension in order to describe them (to describe the tube). However if the strings have no thickness (always unity) then there is no need for the 11th dimension.
In any case, in all currently competing theories, this Dark Matter is strings vibrating in six extra spatial dimensions. And in all those theories gravity is a force carried by gravitons (just like magnetism is carried by photons). Gravitons are emitted from strings and
are then absorbed by other strings even those vibrating in other dimensions (different colors in this presentation). The place where gravitons travel is called the bulk (different than the 2D plane where light travels in this presentation).
From a physics point of view, we are not living in a "Universe" but rather in a "Multiverse"; several universes superimposed above each other. Gravity is the only thing shared between these parallel universes:
The invisible Dark Matter is simply mass in other dimensions. You might ask how does those six extra spatial dimensions look like:
Extra dimensions are tiny and curled up at each point in space. To envision a single extra dimension imagine the ant in the above video shrinking billions of times. Then this ant becomes small enough for transition to the extra circular dimension (like a roller coaster):
However instead of one extra circular dimension there are six dimensions and not necessarily circular; but they are all curled up at each point in space. The ant would encounter multiple routes like this:
As long as the ant remains in any of those extra dimensions we would not be able to see the ant nor collide with it but we would still detect its gravity. In M-Theory this Dark Mater is not only mass in other dimensions but they are in parallel universes (where the laws of physics might not be the same as ours). The only thing shared among those superimposed parallel universes is gravity. Add our universe to those parallel universes you get the Multiverse.