Membrane Theory I'm not a physicist or educated mathematician, so please excuse me if my question is scientifically rudimentary. It concerns Membrane Theory. If all open strings are attached to the surface of the D brane, and all matter is ultimately composed of strings, then how do objects move through 3 dimensional space? If their sub components are anchored to the hyper-surface, then how do they physically move? 
 A: Let's start focusing on Bosonic String Theory. There are two kind of strings: open and closed. 
The closed strings can freely propagate in the 26 dimensional space of the theory. The 26 arises from a precise calculation, in order for the theory to be consistent, Lorentz invariant and other stuff. In the spectrum of the closed string there is always a massless spin 2 particle, the graviton, and that's why string theory is forced to be a quantum theory of gravity.
The open strings cannot live alone, as they not conserve energy. The must be attached to something, and this something turn out to be a Dp-brane, a p-dimensional object with a p+1 world volume. Therefore, while the internal part of the open string can oscillate in the full 26-dimensional space-time, the end-points of the string must be attached to a Dp-brane. It's easy to think about an open string attached to a 2-brane (a plane): the end point can only move on the plane, while the internal part can oscillate outside the plane. The branes are actually dynamical object, as everything in gravity theory, but a low energy the act like an infinite mass wall of classical mechanics and they are "frozen". The massless particle of the open string theory is the photon.
To accomodate fermions, that are absent in bosonic theory, one must go to Superstring theory. This theory lives in 10 dimension, so we think that 4 of them are non compact, while 6 dimension are compactified and invisible to low energy physics.
This a bit beyond the original question, but one step further is to go to the strong  string coupling ($g_s>>1$) where it seems like a new dimension open up and the fundamental theory appears to be an 11-dimensional theory: M-theory. In this theory the fundamental object are not string, but 2 dimensional membranes (and the magnetic dual, the 5-brane). At weak coupling the new dimension close and from the membrane you recover the string of superstring theory (IIA for precision). So in M-theory one must study the propagation of a membrane in 11-dimensional dynamically curved space, a very difficult task that is still work in progress.
