brane

The term brane is used in cosmology to indicate a mathematical object of some number of dimensions, the term typically used for such an object embedded within an object of more dimensions, the latter object sometimes referred to as the bulk. These terms don't imply any more about the objects (rather general terms, much like the mathematical terms subset and set), though given the subject matter, a discussed brane or bulk typically has a lot of internal structure. They allow theorists to save words, speaking of "this brane" and "that brane" rather than "this multidimensional object", etc. The term was coined for physical theories and cosmology that include such a hierarchy of dimensions, inspired by the word "membrane", considering membranes as a two-dimensional objects embedded within the three-dimensional space in which we live. The term brane cosmology (or brane world cosmology) refers to cosmological theories incorporating such embedded branes.

The typical use of the term brane is for the four dimensions of the universe, i.e., spacetime, in discussions of cosmologies that include additional dimensions, when the theory presumes spacetime is embedded in such an object of more dimensions. (I believe the general idea is the brane is connected/continuous within the larger object.) The brane has internal structure, e.g., a brane representing our spacetime has all the characteristics of our spacetime and everything in it. The terms 2-brane, 3-brane, and 4-brane refer to branes of those number of dimensions. Theoretical physicists quite readily describe and analyze universes using other counts of dimensions, both to explore the mathematics and consequences of a theoretical universe that has those numbers of dimensions in place of our four, and to theorize extra, unseen dimensions as a practical way to describe the physics of our universe: such additional dimension(s) could be simply beyond our senses (or to be more specific, the matter that we know of such as atoms, could be confined to our own spacetime, but other spacetimes could exist some ways down some dimension we don't sense, as in a science fiction story) or could be so strongly curved that they are microscopic and literally too small to perceive.