The Bulk and Brane Cosmology

Also known as hyperspace. Higher-dimensional space that contains all branes. A brane is a lower-dimensional object (relative to the Bulk) that contains a universe where physics is restricted to lower-dimensional operation. A brane can be thought of as a sort of container that provides a coherent substrate for lower-dimensional physics. To give an example, imagine flat beings clinging to the surface of a sheet of paper, living comfortably even as their world drifts and moves in our 3-dimensional space.
Scientifically speaking, dimensions are not a synonym for other worlds. A dimension is a pair of directions, which adds an additional coordinate to the minimum number of coordinates required to describe the position of a point. Locating a point in 2-dimensional space requires 2 coordinates; 3-dimensional objects are described by sets of 3 coordinates, and so on. Higher dimensions are those that we cannot ordinarily detect, because we are unable to move ourselves in them and the matter in our bodies can only observe other objects in our lower-dimensional "slice" of the whole.