In theoretical physics, a membrane, brane, or p-brane is a spatially extended mathematical concept that appears in string theory and its relatives (M-theory and brane cosmology). The variable p refers to the number of spatial dimensions of the brane. That is, a 0-brane is a zero-dimensional pointlike particle, a 1-brane is a string, a 2-brane is a "membrane", etc. Every p-brane sweeps out a (p+1)-dimensional world volume as it propagates through spacetime.
Besides the fundamental string (or F-string) of string theory and its magnetic dual, the NS5-brane, the most important type of branes that appear are the D-branes. Different types of D-branes appear in different theories. Even Dn-branes for n appear in type IIA string theory where as the odd Dp-branes appear in type IIB string theory.
With the development of M-theory, an extra dimension appeared and the fundamental string of string theory became a 2-dimensional membrane called an M2-brane (or supermembrane). Its magnetical dual is an M5-brane. The various branes of string theory are thought to be related to these higher dimensional M5-branes wrapped on various cycles.
The M-theory states that strings of energy could grow into larger membranes or branes up to even the size of the universe. It also goes on to state that these strings need to vibrate in more than three dimensions (6) plus another dimension - time.